Calculus 1: Applications of Derivatives
79 videos • 2,074 views • by Math Problems Solved Craig Faulhaber
1
Related Rates 1: Kite Problem
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Related Rates 2: A Kite Problem
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Related Rates 3: An Expanding Circle of Oil
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Related Rates 4: Gravel expanding a Cone
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Related Rates 5: A Running Baseball Player
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Related Rates 9: A Sliding Ladder
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Related Rates 10: The Shadow of a Lamppost
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Linear Approximation 1: f(x)=x+x^4, a=0
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Linear Approximation 2: f(x)=1/x, a=2
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Linear Approximation 3: f(x)=xsinx, a=2pi
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Linear Approximation 4: Approximate the Value (1.1)^3
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Linear Approximation 5: Approximating cos(.03)
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Linear Approximation 6: Approximating sqrt(25.1)
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Differentials 1: A Differential of a Polynomial
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15
Absolute Max and Min 1: f(x)=x^2-3x+3, [0,4]
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Absolute Max and Min 3: f(x)=sqrt(9-x^2), [-2,2]
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Absolute Max and Min 5: f(x)=x/(x^2+1), [0,4]
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Absolute Max and Min 8: f(x)=xe^(-2x), [0,5]
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Rolle's Theorem 1: f(x)=x^2-6x+2, [1,5]
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Mean Value Theorem 1: f(x)=e^x, [0,1]
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Verify that the Mean Value Theorem is satisfied by f(x)=ln(2x+3), [-3/2,0]. If so, find the c value
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Verify that f(x)=sqrt(9-x^2) [-3,3] satisfies the Mean Value Theorem. Find the c value guaranteed by
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Verify that f(x)=x^3+2x+1 [0,6] satisfies the conditions of the Mean Value Theorem, and find c
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24
Increasing, Decreasing, Local Max, Min, Concavity, Inflection 1: A cubic polynomial function
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25
For the function f(x)=1/(x^2-16) find the horizontal and vertical asymptotes.
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For the function f(x)=x^3/(9-x^2) find the horizontal and vertical asymptotes
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For the function f(x)=(-4x^2+4x-2)/(4x^2+2) find the horizontal and vertical asymptotes
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For the function f(x)= -3/x - sqrt(x) find the horizontal and vertical asymptotes
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True or False: Every ratio of polynomial functions has a vertical asymptote
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30
Construct a rational function whose only asymptotes are y=0, x=-2, and x=5 and contains (1,0) and (0
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Construct a rational function whose asymptotes are y=-3, x=-4 and contains (-1/3,0) and (0,-3/4)
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32
Find the following limit: lim_(x to pi/2-) e^(tanx)
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Use the graph to find the following limit: lim_(x to infty) (4x-2)/(5x-3)
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34
The concentration of salt brine in a tank is C(t) = 30t/(200 + t). What happens as t goes to infty
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35
Find the intervals on a graph of f(x) where the function is concave up and concave down
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36
Applied Optimization 1: Minimize and maximize a sum of squares
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Applied Optimization 2: A rope running between poles
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Applied Optimization 3: Minimize a formula for pulse -- sum of square error
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Applied Optimization 4: Running on Shore vs Swimming to an Island
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Applied Optimization 5: Maximizing the volume of a Suitcase l+w+h=66
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Applied Optimization 6: Minimizing the gas usage of a truck g(v)=av+b/v
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Applied Optimization 7: Maximize and Minimize y - 1/x for x + y = 50
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Applied Optimization 8: Find where y=8-x is closest to the point (0,0) and (1,1)
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Applied Optimization 9 (Edit at end!): Maximizing the area of a Norman window given 20 feet of frame
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Applied Optimization 10: Minimizing the cost of a cat bed
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46
Limits Using L'Hopital 1: Evaluate lim_x to infty e^x / x^3
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Find the limit_(x to infinity) x^3/5 lnx and a bonus problem: limit (x to infty) x^(-3/5) lnx
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48
Evaluate the limit: lim_(x to infty) x^(-3.5/x)
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49
Evaluate the limit using two methods: lim_(x to -7) (x^2-49)/(x+7)
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50
Evaluate the limit using L'Hopital or another method: lim_(t to 0) sin(9t)/(9t)
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51
Evaluate the limit using L'Hopital or another method: lim_(x to infinity) x sin(8/x)
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Evaluate the limit using L'Hopital or another method: lim_(x to infty) x e^(4x), Bonus: x e^(-4x)
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Evaluate the limit using L'Hopital or another method: lim_(x to 0) x^(6/cosx) Bonus: x^(6/sinx)
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Evaluate the limit using L'Hopital lim_(x to infinity) (1 + 1.5/x)^(-5.5x), Bonus (1 + 1/x)^(x)
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55
Find the family of antiderivatives of the function f(x) = 4x^3 + x^2 - 2
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Find the family of antiderivatives of the function f(x) = x^(5/2) + 7x^(1/2)
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Find the family of antiderivatives of the function f(x) = sinx + e^(2x)
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Find the family of antiderivatives of the function f(x) = cos(2x) + 3e^(-4x)
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Find the family of antiderivatives of the function f(x) = 5/x^2.5 + x^10
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Find the family of antiderivatives of the function f(x) = -4.5 / sqrt(x^7)
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Find the family of antiderivatives of the function f(x) = -3sec(x) ( sec(x) - tan(x) ). F(x)=___
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62
Evaluate the integral int ( (.5x^7+4.5)/x^7 ) dx
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Find the family of antiderivatives of f with the given condition f(x) = e^7x - 1.5x^2 and F(0)=8
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Find a function satisfying the conditions f'''(x)=cosx, f(0)=8, f'(0)=0, f''(0)=-1
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Find a function satisfying the conditions f'''(x)=27cos(3x), f(0)=-8, f'(0)=1, f''(0)=3
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Calc POD #38 Related Rates. A circle has an initial radius of 50 ft when the radius begins decre...
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Calc 1 POD #39 Related Rates. A rope passing through a capstan on a dock is attached to a boat...
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Calc 1 POD #40 Critical Points. Find the critical points of the following function f(x)=2x^2−3x−4
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Calculus POD 41 Critical Points. Find the absolute extreme values of f(x)=sin(3x) on [−π/4,π/3]
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Calculus POD #42 Mean Value Theorem Determine whether the Mean Value Theorem applies to...
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Calc 1 POD #43 Find the intervals on which f is increasing and decreasing.f(x)=x^2 ln(x^2) − 2
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Calc POD #44 Second Derivative Test. Locate the critical points of the following function. Then...
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Calc POD 45 Use f′(x)=(x−1)(x+2)(x+5) to determine the local maxima and minima, and intervals...
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Calc POD #46 Optimization: Of all rectangles with a perimeter of 27, which one has the max area?
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Calculus POD 47 Minimum Surface Area of a Tank
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Calc 1 POD #48 Linearizations
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Calculus POD 49 L'Hopital's Rule
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Calculus 1 POD #50 L'Hopitals Rule
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Calculus POD #51 Newton's Method
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