Calculus 1 Videos

555 Video Lessons

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LIMITS – 60 Video Lessons
EVALUATING LIMITS
  1. lim 5 , x -> -1
  2. lim (-x + 2) , x -> -5/2
  3. lim (x^3-x^2-4) , x -> 2
  4. lim (-(x^2)/2 + 2x + 4) , x -> 1
  5. lim -√(x + 3) , x -> 3
  6. lim -√(2x + 4) , x -> 3/2
  7. lim – (x – 4)/(x^2 – 6x + 8) , x -> 1
  8. lim (-x – 3)/(x^2 + x + 1) , x -> 3/2
  9. lim sin(x) , x -> π
  10. lim 2cos(x) , x -> 3π/4
  11. Give an example of a limit that evaluates to 4
  12. Give an example of a limit of a quadratic function where the limit evaluates to 9
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LIMITS AT JUMP DISCONTINUITIES AND KINKS
  1. lim x->-1^+ 4x+4/|x+1|
  2. lim x->-1^- f(x), f(x)={-x-8 when x≤-1; -x^2-4x-4 when x>-1
  3. lim x->-3 f(x), f(x)={-x^2-10x-24 when x≤-3; 2x+3 when x>-3
  4. lim x->-1 f(x), f(x)={x when x<-1; -x^2+2x when x≥-1
  5. lim x->-1^- f(x), f(x)={-x-3 when x≤-1; x+1 when x>-1
  6. lim x->-2 f(x), f(x)={-x^2-4x-5 when x≤-2; -1 when x>-2
  7. lim x->0^+ f(x), f(x)={1 when x≤0; -x^2+4x-3 when x<0
  8. lim x->0^- |x|/x
  9. lim x->0^+ floor(-2x+1)
  10. lim x->1 f(x), f(x)={x/2+9/2 when x<1;x^2-6x+10 when x≥1
  11. lim x->-1 3|x+1|/(x+1)
  12. lim x->-2 f(x), f(x)={x^2 when x≤-2; -x/2+3 when x>-2
  13. Give an example of a two-sided limit of a piecewise function where the limit does not exist.
  14. Give an example of a two-sided limit of a function with an absolute value where the limit does not exist.
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LIMITS AT REMOVABLE DISCONTINUITIES
  1. lim x->2 f(x) where f(x)={-x^2+2 when x≠2; -5 when x=2
  2. lim x->-2 -(x^2-4)/(x+2)
  3. lim x->3 (x^2-7x+12)/(x-3)
  4. lim x->-3 (x+3)/(x^2+2x-3)
  5. lim x->0 f(x) where f(x)={x+1 when x≠0; 2 when x=0
  6. lim x->3 f(x) where f(x)={2+x/2 when x≠3; 2 when x=3
  7. lim x->1 -(x^2-1)/(x-1)
  8. lim x->5 -(x^2-5x)/(x-5)
  9. lim x->2 -(x^2-x-2)/(x-2)
  10. lim x->-5 (x^2+3x-10)/(x+5)
  11. lim x->0 ((1/(-4+x))+1/4)/x
  12. lim x->-3 x/((1/(3+x))-1/3)
  13. lim x->5 (x-5)/(√(x+4)-3)
  14. lim x->3 (√(x+6)-3)/(x-3)
  15. Give an example of a limit of a rational function where the limit at -1 exists, but the rational function is undefined at -1.
  16. Give two values of a where the limit cannot be solved using direct evaluation. Give one value of a where the limit can be solved using direct evaluation. lim x->a x/((1/(-2+x))+1/2)
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LIMITS AT ESSENTIAL DISCONTINUITIES
  1. lim x->-3^+ (x+2)/(x^2+5x+6)
  2. lim x->-4 (x^2)/(4x+16)
  3. lim x->-2^+ 3x/(x+2)
  4. lim x->-1^+ (x^2)/(x+1)
  5. lim x->-3^- 2x/(x+3)
  6. lim x->-2^+ 1/(x^2-4)
  7. lim x->3^- -4x/(x-3)
  8. lim x->1 -3/(x-1)
  9. lim x->-2^- (x+2)/(x^2+x-2)
  10. lim x->-3^- -2/(x+3)
  11. lim x->π/4^- 2sec(2x)
  12. lim x->3π/4^+ 2tan(2x)
  13. Give an example of a right-sided limit that goes to ∞ as x goes to 5.
  14. Give an example of a left-sided limit that goes to ∞ as x goes to 5.
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CONTINUITY – 17 Video Lessons
CONTINUITY
  1. f(x)={x^2+2x+1 when x<1; -x/2 when x≥1
  2. f(x)={1 when x≠5; 3 when x=5
  3. f(x)={2x-10 when x<2; 0 when x≥2
  4. f(x)=(x^2-x-2)/(x+1)
  5. f(x)=(x^2)/(2x+4)
  6. f(x)=-x/2-7/2 when x≤0; -x^2+2x-2 when x>0
  7. f(x)=-(x^2-x-12)/(x+3)
  8. f(x)=(x^2-x-6)/(x+2)
  9. f(x)=-(x^2)/(2x+4)
  10. f(x)=(x+1)/(x^2-x-2)
  11. f(x)=(x+1)/(x^2+x+1)
  12. f(x)=-(x^2)/(x-1)
  13. f(x)={x^2-4x+3 when x≠0; 3 when x=0
  14. f(x)={-x^2 when x≠1; 0 when x=1
  15. Give an example of a function with discontinuities at x=1, 2, and 3.
  16. Of the six basic trigonometric functions, which are continuous over all real numbers? Which are not? What types of discontinuities are there?
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DIFFERENTIATION – 147 Video Lessons
AVERAGE RATES OF CHANGE
  1. y=x^2-x+1; [0,3]
  2. y=-1/(x-2); [-3,-2]
  3. y=-x^2+x+2; (-2,-4), (1,2)
  4. y=-1/x; (1,-1), (3,-1/3)
  5. y=x^2+2; [-2,-3/2]
  6. y=2x^2-2x+1; [-1,-1/2]
  7. y=-1/(x+2); [-1,-1/2]
  8. y=2x^2+x+2; [0,1/2]
  9. y=-x^2-2; (1,-3), (3/2,17/4)
  10. y=1/(x+3); (-1,1/2), (-1/2,2/5)
  11. y=1/(x-1); (-2,-1/3), (-3/2,-2/5)
  12. y=-1/x; (1,-1), (3/2,-2/3)
  13. The police have accused a driver of breaking the speed limit of 60 miles per hour. As proof, they provide two photographs. One photo shows the driver’s car passing a toll booth at exactly 6 PM. The second photo shows the driver’s car passing another toll booth 31 miles down the highway at exactly 6:30 PM. Does the photo evidence prove that the driver broke the speed limit during this time?
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DEFINITION OF THE DERIVATIVE
  1. y=-2x+5
  2. f(x)=-4x-2
  3. y=4x^2+1
  4. f(x)=-3x^2+4
  5. y=-4x^2-5x-2
  6. y=3x^2+3x+3
  7. y=√(-3x-5)
  8. f(x)=√(4x-5)
  9. y=1/(x+2)
  10. f(x)=-2/(2x-1)
  11. Use the definition of the derivative to show that f'(0) does not exist where f(x)=|x|.
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INSTANTANEOUS RATES OF CHANGE
  1. y=2x^2-2; [1, 3/2]
  2. y=-1/(x-3); [0, 1/2]
  3. y=x^2+x+2; (-1, 2), (-1/2, 7/4)
  4. y=1/(x+2); (-1, 1), (-1/2, 2/3)
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POWER, CONSTANT, AND SUM RULES
  1. ​​y = 5
  2. ​f(x) = 5x^18
  3. y = 4x^5 + x
  4. f(x) = 4x^4 – 5x – 3
  5. y = 3x^(5/4)
  6. y = (5/4)x^(2/3)
  7. y = -4x^-5
  8. y = 3/x^3
  9. y = x^(2/3)
  10. f(x) = -2 fourth root (x)
  11. y = (2/3)x^4 + 5x – x^-3
  12. y = (-1/2)x^4 + 3x^(5/3) + 2x
  13. y = -3r^5 – 5r^2
  14. f(s) = (-3/s^2) – (4/s^4)
  15. ​f(x) = (2/3)x^(3/2) – (3/4)x^(3/5)
  16. h(s) = sqrt(2)cbrt(s) + sqrt(2)5th-rt(s)
  17. y = 5c
  18. y = 4ax^3a – bx^3c
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HIGHER ORDER DERIVATIVES
  1. y = -x^2 find d^2y/dx^2
  2. ​f(x) = 4x^3 find f”
  3. y = -4x find d^3y/dx^3
  4. ​f(x) = 5x^4 find f”’
  5. y = -5x^4 find d^4y/dx^4
  6. y = 3x^5 – 2x find d^3y/dx^3
  7. ​y = -2x^3 – 4x^-3 find d^3y/dx^3
  8. y = -x^2 + 2(5th-rt(x^2)) find d^3y/dx^3
  9. ​y = 99x^99 find d^100y/dx^100
  10. f(x) = x^99 find f^(99)
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DIFFERENTIATION – PRODUCT RULE
  1. y = -x^3(3x^4 – 2)
  2. f(x) = x^2(-3x^2 – 2)
  3. y = (-2x^4 – 3)(-2x^2 + 1)
  4. f(x) = (2x^4 – 3)(x^2 + 1)
  5. f(x) = (5x^5 + 5)(-2x^5 – 3)
  6. f(x) = (-3 + x^-3)(-4x^3 + 3)
  7. y = (-2x^4 + 5x^2 + 4)(-3x^2 + 2)
  8. y = (x^4 + 3)(-4x^5 + 5x^4 + 5)
  9. y = (5x^4 – 3x^2 – 1)(-5x^2 + 3)
  10. y = (-10x^2 – 7(5th rt(x^2)) + 9)(2x^3 + 4)
  11. ​y = (5 + 3x^-2)(4x^5 + 6x^3 + 10)
  12. ​y = (-6x^4 + 2 + 6x^-4)(6x^4 + 7)
  13. ​​f(x) = (-7x^4 + 10x^2/5 + 8)(x^2 + 10)
  14. ​​Prove (f • g)’ ≠ f’ • g’ for any functions f and g
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DIFFERENTIATION – QUOTIENT RULE
  1. f(x) = 2/(2x^4 – 5)
  2. f(x) = 2/(x^5 – 5)
  3. f(x) = 5/(4x^3 + 4)
  4. y = (4x^3 – 3x^2)/(4x^5 – 4)
  5. y = (3x^4 + 2)/(3x^3 – 2)
  6. y = (4x^5 + 2x^2)/(3x^4 + 5)
  7. y = (4x^5 + x^2 + 4)/(5x^2 – 2)
  8. y = (3x^4 + 5x^3 – 5)/(2x^4 – 4)
  9. ​y = (x^3 – x^2 – 3)/(x^5 + 3)
  10. ​y = (x^4 + 6)/(3 – 4x^-4)
  11. y = (4x^4 – 4x^2 + 5)/(2x^5/3 + 3)
  12. ​​Prove (f/g)’ ≠ f’/g’ for any functions f and g
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DIFFERENTIATION – CHAIN RULE
  1. y = (x^3 + 3)^5
  2. ​y = (-3x^5 + 1)^3
  3. ​​y = (-5x^3 – 3)^3
  4. ​y = (5x^2 + 3)^4
  5. ​f(x) = 4th-rt(-3x^4 – 2)
  6. ​f(x) = sqrt(-2x^2 + 1)
  7. ​f(x) = cbrt(-2x^4 + 5)
  8. ​​y = (-x^4 – 3)^-2
  9. ​y = (3x^3 + 1)(-4x^2 – 3)^4
  10. ​y = ((x^3 + 4)^5)/(3x^4 – 2)
  11. ​y = ((x + 5)^5 – 1)^4
  12. ​y = (5x^3 – 3)^5((4th-rt(-4x^5 – 3))
  13. ​Give a function that requires three applications of the chain rule and differentiate
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DIFFERENTIATION – TRIG FUNCTIONS
  1. f(x) = sin 2x^3​​​
  2. y = tan 5x^3
  3. y = sec 4x^5
  4. y = csc 5x^5
  5. y = (2x^5 + 3)cos x^2
  6. y = (-2x^2 – 5) / cos 2x^3
  7. f(x) = sin^3 x^5
  8. f(x) = cos (-3x^2 + 2)^2
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DIFFERENTIATION – INVERSE TRIG
  1. y = cos^-1(-5x^3)
  2. y = sin^-1(-2x^2)
  3. y = tan^-1(2x^4)
  4. y = csc^-1(4x^2)
  5. y = (sin^-1(5x^2))^3
  6. y=sin^-1(3x^5+1)^3
  7. y=(cos^-1(4x^2))^2
  8. y=cos^-1(-2x^3-3)^3
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DIFFERENTIATION – NATURAL LOGS AND EXPONENTIALS
  1. y = ln(x^3)
  2. y = e^(2x^3)
  3. y = ln(ln(2x^4)
  4. y = ln(ln(3x^3)
  5. y = cos(ln(4x^3)
  6. y = e^(e^(3x^2))
  7. y = e^((4x^3 + 5)^2)
  8. y = ln(4x^2) • (-x^3 – 4)
  9. y = ln((- (4x^4)/(x^3 – 3))^5)
  10. y = (e^(5x^4))/(e^(4x^2 + 3))
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IMPLICIT DIFFERENTIATION
  1. 2x^3 = 2y^2 + 5
  2. 3x^2 + 3y^2 = 2
  3. 5y^2 = 2x^3 – 5y
  4. 4x^2 = 2y^3 + 4y
  5. 5x^3 = -3xy + 2
  6. 1 = 3x + 2x^2y^2
  7. 3x^2y^2 = 4x^2 – 4xy
  8. 5x^3 + xy^2 = 5x^3y^3
  9. 2x^3 = (3xy + 1)^2
  10. x^2 = (4x^2y^3 + 1)^2
  11. sin 2x^2y^3 = 3x^3 +1
  12. 3x^2 + 3 = ln 5xy^2
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APPLICATIONS OF DIFFERENTIATION – 136 Video Lessons
DERIVATIVE AT A VALUE
  1. y=x^2+4x at x=5
  2. y=-x^3+4x^2-4 at x=4
  3. y=20/(x^2+5) at x=3
  4. y=2/(x+1) at x=5
  5. y=(-x+4)^1/2 at x=0
  6. y=(-3x+9)^1/2 at x=5
  7. y=e^(-x+2) at x=4
  8. y=-ln(x+3) at x=5
  9. y=2sin(2x) at x=-π/2
  10. y=-tan(2x) at x=-π
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SLOPE AT A VALUE
  1. y=x^2+6x+7 at x=-2
  2. y=x^3-3x^2+5 at x=3
  3. y=x^3-6x^2+9x-4 at x=2
  4. y=-x^3-6x^2-9x+1 at x=-4
  5. y=-1/(x^2-9) at x=2
  6. y=-3/(x+5) at x=1
  7. y=-(x+2)^(1/2) at x=-1
  8. y=-(-x+2)^(1/2) at x=-5
  9. y=-ln(-x+2) at x=-3
  10. y=sin(2x) at x=-π
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TANGENT LINES
  1. y=x^3-3x^2+2 at (3,2)
  2. y=-5/(x^2+1) at (-1,-5/2)
  3. y=x^3-2x^2+2 at (2,2)
  4. y=-3/(x^2-25) at (-4,1/3)
  5. y=-3/(x^2-4) at (1,1)
  6. y=(5x+5)^(1/2) at (4,5)
  7. y=ln(-x) at (-2,ln 2)
  8. y=-2tan(x) at (-π,0)
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NORMAL LINES
  1. y=x^3-x^2-2 at (1,-2)
  2. y=1/(x-4) at (5,1)
  3. y=-x^3+15x^2-72x+110 at (4,-2)
  4. y=2/(x-3) at (5,1)
  5. y=3/(x+2) at (4,1/2)
  6. y=(2x-8)^(1/3) at (0,-2)
  7. y=ln(x+4) at (-3,0)
  8. y=-sin(2x) at (-π/2,0)
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HORIZONTAL TANGENTS
  1. y=-x^2-4x-6
  2. y=-x^3+3x^2-1
  3. y=-x^3+x^2-2
  4. y=1/(x^2-1)
  5. y=x^3-2x^2+2
  6. y=-x^3+(9x^2/2)-12x-3
  7. y=-2/(x-3)
  8. y=-1/(x^2+1)
  9. y=(-2x+4)^(1/2)
  10. y=-csc(x); [-π, π]
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ROLLE’S THEOREM
  1. y=x^2+4x+5; [-3,-1]
  2. y=x^3-2x^2-x-1; [-1,2]
  3. y=-x^3+2x^2+x-6; [-1,2]
  4. y=x^3-4x^2-x+7; [-1,4]
  5. y=-x^3+2x^2+x-1; [-1,2]
  6. y=x^3-x^2-4x+3; [-2,2]
  7. y=(-x^2-2x+15)/(-x+4); [-5,3]
  8. y=(x^2-2x-15)/(-x+6); [-3,5]
  9. y=(-x^2+2x+15)/(x+4); [-3,5]
  10. y=(x^2+x-6)/(-x+3); [-3,2]
  11. y=-2sin(2x); [-π,π]
  12. y=sin(2x); [-π,π]
  13. y=(x^2-x-12)/(x+4); [-3,4]
  14. y=(-x^2-2x+8)/(-x+3); [-4,2]
  15. y=(-x^2+36)/(x+7); [-6,6]
  16. y=(-x^2+4)/(4x); [-2,2]
  17. y=2tan(x); [-π,π]
  18. y=-2cos(2x); [-π,π]
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MEAN VALUE THEOREM
  1. y=-x^2+8x-17; [3,6]
  2. y=x^3-9x^2+24x-18; [2,4]
  3. y=-(x^2/2)+x-1/2; [-2,1]
  4. y=(x^2/2)-2x-1; [-1,1]
  5. y=x^3+3x^2-2; [-2,0]
  6. y=-x^3+4x^2-3; [0,4]
  7. y=(x^2-9)/3x; [1,4]
  8. y=x^2/(2x-4); [-4,1]
  9. y=-(-2x+6)^(1/2); [-2,3]
  10. y=-(-5x+25)^(1/2); [3,5]
  11. y=-x^2/(4x+8); [-3,-1]
  12. y=(-x^2+9)/4x; [1,3]
  13. y=-(6x+24)^(2/3); [-4,-1]
  14. y=(x-3)^(2/3); [1,4]
  15. Use the Mean Value Theorem to prove that |sin(a)-sin(b)| ≤ |a-b| for all real values of a and b where a≠b.
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INTERVALS OF INCREASE AND DECREASE
  1. y=-x^3+2x^2+2
  2. y=x^3-11x^2+39x-47
  3. y=-x^4+3x^2-3
  4. y=x^2/(4x+4)
  5. y=(3x^2-3)/x^3
  6. y=(2x-8)^(2/3)
  7. y=-(1/5)(x-4)^(5/3)-2(x-4)^(2/3)-1
  8. If functions f and g are increasing on an interval, show that f+g is increasing on the same interval.
  9. Give an example where functions f and g are increasing on the interval (-∞,∞), but where f–g is decreasing.
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INTERVALS OF CONCAVITY
  1. y=x^3-3x^2+4
  2. y=x^3-2x^2-2
  3. y=x^4+x^3-3x^2+1
  4. y=1/(x-3)
  5. y=-x^3/(x^2-4)
  6. y=(5x+30)^(2/3)
  7. y=-(3/16)(x-1)^(4/3)-(3/2)(x-1)^(1/3)+2
  8. Sketch a continuous curve y=f(x) where f(1)=0, f'(0)=0, f'(2)=0, f”(x)<0 for x<1, and f”(x)>0 for x>1.
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RELATIVE EXTREMA
  1. y=x^3-5x^2+7x-5
  2. y=x^3-6x^2+9x+1
  3. y=-x^3-3x^2-1
  4. y=x^4-2x^2+3
  5. y=x^4-x^2
  6. y=-2/(x^2-4)
  7. y=(2x-8)^(2/3)
  8. y=-(1/5)(x-4)^(5/3)-2(x-4)^(2/3)
  9. Give an example function f(x) where f”(0)=0 and there is no relative minimum or maximum at x=0.
  10. Give an example function f(x) where f”(0)=0 and there is no relative maximum at x=0.
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ABSOLUTE EXTREMA
  1. y=-x^3-6x^2-9x+3; [-3,-1]
  2. y=8/(x^2+4); [0,5]
  3. y=x^3+6x^2+9x+3; [-4,0]
  4. y=x^4-3x^2+4; [-1,1]
  5. y=x^2/(3x-6); [3,6]
  6. y=(x+2)^(2/3); [-4,-2]
  7. y=x^3-3x^2-3; (0,3)
  8. y=(5x+25)^(1/3); [-2,2]
  9. y=x^3-3x^2+6; [0,∞)
  10. y=x^4-2x^2-3; (0,∞)
  11. y=4/(x^2+2); (-5,-2]
  12. y=-(1/6)(x+1)^(7/3)+(14/3)(x+1)^(1/3); (-5,0)
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RELATED RATES
  1. Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 5 cm?
  2. Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The area of the spill increases at a rate of 9π m^2/min. How fast is the radius of the spill increasing when the radius is 10 m?
  3. A conical paper cup is 10 cm tall with a radius of 10 cm. The cup is being filled with water so that the water level rises at a rate of 2 cm/sec. At what rate is water being poured into the cup when the water level is 8 cm?
  4. A spherical balloon is inflated so that its radius (r) increases at a rate of 2/r cm/sec. How fast is the volume of the balloon increasing when the radius is 4 cm?
  5. A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person’s shadow changing when the person is 16 ft from the lamppost?
  6. An observer stands 700 ft away from a launch pad to observe a rocket launch. The rocket blasts off and maintains a velocity of 900 ft/sec. Assume the scenario can be modeled as a right triangle. How fast is the observer to rocket distance changing when the rocket is 2400 ft from the ground?
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INDEFINITE INTEGRATION – 99 Video Lessons
INTEGRATION POWER RULE
  1. ​​∫-24x^5 dx
  2. ∫-3 dx
  3. ∫-6x dx
  4. ∫12x^2 dx
  5. ∫(-24x^5 – 10x) dx
  6. ∫(-9x^2 +10x) dx
  7. ∫4x^-5 dx
  8. ∫-2x^-3 dx
  9. ∫(-2x^-3 + 20x^-5) dx
  10. ∫(-4x^-3 – 20x^-5) dx
  11. ∫(-(4/x^3) – (8/x^5)) dx
  12. ∫((15/x^4) + (8/x^5)) dx
  13. ∫-(14x^(5/2))/2 dx
  14. ∫-(35x^(2/5))/5 dx
  15. ∫-(5cbrt(x^2))/3 dx
  16. ∫-(5•4th rt(x))/2 dx
Compile Video
INTEGRATION – LOGARITHMIC RULE AND EXPONENTIALS
  1. ∫x^-1 dx
  2. ∫3x^-1 dx
  3. ∫-(1/x) dx
  4. ∫1/x dx
  5. ∫-e^x dx
  6. ∫e^x dx
  7. ∫2•3^x dx
  8. ∫3•5^x dx
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INTEGRATION TRIG FUNCTIONS
  1. ​​∫cos(x) dx
  2. ∫-5sin(x) dx
  3. ∫3•sec^2(x) dx
  4. ∫-3csc(x)•cot(x) dx
  5. ∫2/sec(x) dx
  6. ∫5/csc(x) dx
  7. ∫-4tan(x) dx
  8. ∫-cot(x) dx
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INTEGRATION INVERSE TRIGONOMETRIC FUNCTIONS
  1. ∫1/√(16-x^2) dx
  2. ∫1/(4+x^2) dx
  3. ∫1/(x√(x^2-1)) dx
  4. ∫1/(16+x^2) dx
  5. ∫1/(x√(x^2-4)) dx
  6. ∫1/√(25-x^2) dx
  7. ∫1/(x√(x^2-81)) dx
  8. ∫1/(4+x^2) dx
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INTEGRATION BY SUBSTITUTION (POWER RULE)
  1. ∫-15x^4(-3x^5-1)^5 dx; u=-3x^5-1
  2. ∫-16x^3(-4x^4-1)^-5 dx; u=-4x^4-1
  3. ∫-(8x^3)/((-2x^4+5)^5) dx; u=-2x^4+5
  4. ∫(5x^4+5)^(2/3)•20x^3 dx; u=5x^4+5
  5. ∫((5+ln(x))^5)/x dx; u=5+ln(x)
  6. ∫4sec(4x)•tan(4x)•sec^4(4x) dx; u=sec(4x)
  7. ∫36x^3(3x^4+3)^5 dx; u=3x^4+3
  8. ∫x(4x-1)^4 dx; u=4x-1
  9. ∫-9x^2(-3x^3+1)^3 dx
  10. ∫12x^3(3x^4+4)^4 dx
  11. ∫-12x^2(-4x^3+2)^-3 dx
  12. ∫(3x^5-3)^(3/5)•15x^4 dx
  13. ∫(-2x^4-4)^4•-32x^3 dx
  14. ∫(e^4x-4)^(1/5)•8e^4x dx
  15. ∫x(4x+5)^3 dx
  16. ∫5x√(2x+3) dx
Compile Video
INTEGRATION BY SUBSTITUTION (LOGARITHMS AND EXPONENTIALS)
  1. ∫20x^4/(4x^5+3) dx; u=4x^5+3
  2. ∫36x^2e^(4x^3+3) dx; u=4x^3+3
  3. ∫80x^3•3^(5x^4-2) dx; u=5x^4-2
  4. ∫2/(x(-1+ln(4x))) dx; u=-1+ln(4x)
  5. ∫12x^2/(x^3+2) dx
  6. ∫20e^5x/(e^(5x)+3) dx
  7. ∫10sin(-2x)•e^(cos(-2x)) dx
  8. ∫(5e^(-3+ln(3x)))/x dx
Compile Video
INTEGRATION BY SUBSTITUTION (TRIG FUNCTIONS)
  1. ∫20xsin(5x^2-3) dx; u=5x^2-3
  2. ∫16x^3•sec^2(4x^4-2) dx; u=4x^4-2
  3. ∫6e^(3x)cos(e^(3x)-5) dx; u=e^(3x)-5
  4. ∫(50x)/(sec(5x^2+5) dx; u=5x^2+5
  5. ∫-36x^3sec(3x^4+3)•tan(3x^4+3) dx
  6. ∫-9sec(-3x)•tan(-3x)•sec^2(sec(-3x)) dx
  7. ∫-(5cos(-4+ln(4x)))/x dx
  8. ∫(4x^3)/(csc(x^4-1) dx
Compile Video
INTEGRATION BY SUBSTITUTION (INVERSE TRIG FORMS)
  1. ∫20x^3/√(25-25x^8) dx; u=5x^4
  2. ∫10x^4/(9+4x^10) dx; u=2x^5
  3. ∫-(2•csc^2(2x))/(cot(2x)•√(cot^2(2x)-1)) dx; u=cot(2x)
  4. ∫1/(x√(25-(ln(-2x))^2)) dx; u=cot(2x)
  5. ∫8x/√(9-16x^4) dx
  6. ∫3x^2/(x^3√(x^6-1)) dx
  7. ∫10x/(16+25x^4) dx
  8. ∫-(4sin(4x))/√(9-cos^2(4x)) dx
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INTEGRATION BY PARTS
  1. ∫xe^x dx; u=x, dv=e^x dx
  2. ∫xcos(x) dx; u=x, dv=cos(x) dx
  3. ∫x•2^x dx; u=x, dv=2^x dx
  4. ∫√(x)ln(x) dx; u=ln(x), dv=√(x) dx
  5. ∫xe^(-x) dx
  6. ∫x^(2)cos(3x) dx
  7. ∫(x^2)/(e^(2x)) dx
  8. ∫x^(2)e^(5x) dx
  9. ∫ln(x+3) dx
  10. ∫cos(2x)•e^(-x) dx
Compile Video
DEFINITE INTEGRATION – 75 Video Lessons
APPROXIMATING AREA UNDER A CURVE
  1. y=(x^2/2)+x+2; [-5, 3]
  2. y=x^2+3; [-3, 1]
  3. y=-(x^2/2)+6; [-3, 2]
  4. y=-(x^2/2)+x+5; [-1, 4]
  5. y=-x+5; [-7, -5]
  6. y=2/x; [1, 5]
  7. y=-x^2+2x+11; [-1, 3]
  8. y=x^2-2x+3; [-1, 3]
Compile Video
AREA UNDER A CURVE USING LIMITS OF SUMS
  1. ∑ from k=1 to n of 18k
  2. ∑ from k=1 to n of (2k+5)
  3. ∑ from k=1 to n of 8k^2
  4. ∑ from k=1 to n of (k^2+4)
  5. lim as n->∞ ∑ from k=1 to n of ((2/n)+(2k/n^2))
  6. lim as n->∞ ∑ from k=1 to n of ((5/n)+(k^3/n^4))
  7. f(x)=3x+3; [0,3]
  8. f(x)=x^2+5; [1,3]
Compile Video
RIEMANN SUM TABLES
  1. ∫f(x) dx 0->10 where x=0, 2, 5, 7, 10 and f(x)=2, 3, 5, 7, 8
  2. ∫f(x) dx 0->10 where x=0, 4, 6, 7, 10 and f(x)=5, 3, 2, 3, 5
  3. ∫f(x) dx 0->14 where x=0, 3, 5, 9, 13, 14 and f(x)=-1, -2, -1, 0, -1, 0
  4. ∫f(x) dx 0->19 where x=0, 4, 9, 10, 12, 19 and f(x)=-3, -5, -4, -2, -1, 1
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FIRST FUNDAMENTAL THEOREM OF CALCULUS
  1. ∫(-x^3+3x^2+1) dx from -1 to 3
  2. ∫(x^4+x^3-4x^2+6) dx from -2 to 1
  3. ∫(2x^2-12x+13) dx from 1 to 3
  4. ∫(-x^3+3x^2-2) dx from 0 to 3
  5. ∫(x^5-4x^3+4x+4) dx from -1 to 0
  6. ∫4x^(1/3) dx from -3 to 0
  7. ∫-(4/x^3) dx from -4 to -1
  8. ∫4/x dx from -3 to -1
  9. ∫2cos(x) dx from (-π/4) to (-π/6)
  10. ∫1/(x√(x^2-1) dx from √2 to 2
  11. ∫5(2x+4)^(1/3) dx from -3 to -2
  12. ∫2/(2x+4)^3 dx from -1 to 2
  13. ∫e^(2x-2) dx from -1 to 1
  14. ∫(-x+|-3x-9|) dx from -4 to -2
  15. ∫f(x) dx from 0 to 3 where f(x)={x/2-1 when x≤2, x^2-6x+8 when x>2
  16. ∫-|x^2+4x| dx from -5 to 1
Compile Video
SUBSTITUTION FOR DEFINITE INTEGRALS
  1. from -1 to 0 ∫8x/(4x^2+1)^2 dx; u=4x^2+1 
  2. from 0 to 1 ∫-12x^2(4x^3-1)^3 dx; u=4x^3-1
  3. from -1 to 2 ∫6x(x^2-1)^2 dx; u=x^2-1
  4. from 0 to 1 ∫24x/(4x^2+4)^2 dx; u=4x^2+4
  5. from -3 to 0 ∫-8x/(2x^2+3)^2 dx; u=2x^2+3
  6. from 0 to 1 ∫16x/(4x^2+4)^2 dx; u=4x^2+4
  7. from -1 to 0 ∫18x^2(3x^3+3)^2 dx; u=3x^3+3
  8. from 0 to 1 ∫-8x/(4x^2+2)^2 dx; u=4x^2+2
Compile Video
MEAN VALUE THEOREM FOR INTEGRALS
  1. f(x)=-x^2-2x+5; [-4,0]
  2. f(x)=-x^4+2x^2+4; [-2,1]
  3. f(x)=-x^2/2+x+3/2; [-3,1]
  4. f(x)=4/x^2; [-4,-2]
  5. f(x)=-x^3+7x^2-11x+3; [1,5]
  6. f(x)=-x^5+3x^3; [0,1]
  7. f(x)=4x^(1/2); [0,3]
  8. f(x)=x^5-2x^3+x; [-1,0]
  9. f(x)=1/x; [2,3]
  10. f(x)=x^5-4x^3+2x-1; [-2,2]
  11. f(x)=-x^5+4x^3-5x-3; [-2,0]
  12. f(x)=x^5-2x^3-2; [-1,1]
  13. f(x)=-x+2; [-2,2]
  14. f(x)=-x^2-8x-17; [-6,-3]
  15. f(x)=-3(2x-6)^(1/2); [3,5]
  16. f(x)=4/(2x+6)^2; [-6,-5]
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SECOND FUNDAMENTAL THEOREM OF CALCULUS
  1. F(x)=∫ from -4 to x of (t-1) dt
  2. F(x)=∫ from -3 to x of (t^2+2t+3) dt
  3. F(x)=∫ from -1 to x^2 of (-2t+2) dt
  4. F(x)=∫ from 4 to 3x of (-t^3+11t^2-39t+44) dt
  5. F(x)=∫ from 2 to x^2 of (1/t^3) dt
  6. F(x)=∫ from x to x^2 of (-2t-2) dt
  7. F(x)=∫ from x to x^2 of (t^2-8t+11) dt
  8. F(x)=∫ from x to 2x of (2/t) dt
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APPLICATIONS OF INTEGRATION – 14 Video Lessons
AREA UNDER A CURVE
  1. y=4/x^2; [-2, -1]
  2. y=sec^2(x); [-π, -3π/4]
  3. y=√x; [4, 5]
  4. y=-cos(x); [3π/4, π]
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AREA BETWEEN CURVES
  1. y=2x^2-8x+10, y=x^2/2-2x-1, x=1, x=3
  2. x=2y^2+12y+19, x=-y^2/2-4y-10, y=-3, y=-2
  3. y=x^2/2-3x-1/2, y=3
  4. y=-x^3/2+2x^2, y=-x^2+4x
  5. y=-2x^2-1, y=-x+3, x=0, x=1
  6. y=2cbrt(x^2), y=x
  7. y=-x^3+6x, y=-x^2
  8. y=-2*sec^2(x), y=2cos(x), x=0, x=π/4
Compile Video
MISCELLANEOUS – 7 Video Lessons

MISCELLANEOUS

  1. Power Rule
  2. Basic Graph Transformations
  3. Basic Composite Functions
  4. Showing a Limit Exists
  5. Showing a Limit Does Not Exist
  6. ​The Product Rule
  7. ​Differentiate y=x^2sin(x)
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