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Questions and Answers
Which of the following statements is FALSE?
Which of the following statements is FALSE?
- The linear approximation of y at x=c is f(c) + f'(c)(x-c).
- When the change in x is sufficiently small, we can approximate the change in y with its differential.
- The differential of y is f'(x)(Δx). (correct)
- The exact change in y is equal to f(x+Δx) - f(x).
Estimate the value of √4.4 using differentials.
Estimate the value of √4.4 using differentials.
- 2.05
- 2.2
- 2.15
- 2.1 (correct)
The speed at which the volume of a cone is changing is given by
The speed at which the volume of a cone is changing is given by
- $\frac{dV}{dt} = \frac{2\pi rh}{3} \frac{dr}{dt} + \frac{\pi r^2}{3} \frac{dh}{dt}$ (correct)
- $\frac{dV}{dt} = 2\pi rh \frac{dr}{dt} + \pi r^2 \frac{dh}{dt}$
- $\frac{dV}{dt} = \frac{2\pi rh}{3} \frac{dh}{dt} + \frac{\pi r^2}{3} \frac{dr}{dt}$
- $\frac{dV}{dt} = 2\pi rh \frac{dh}{dt} + \pi r^2 \frac{dr}{dt}$
A hollow cylinder is made by punching a concentric hole through a solid cylinder of radius = 5 cm and height = 10 cm. If the radius of the hole is 0.3cm smaller than the cylinder's radius, estimate the volume of the hollow cylinder.
A hollow cylinder is made by punching a concentric hole through a solid cylinder of radius = 5 cm and height = 10 cm. If the radius of the hole is 0.3cm smaller than the cylinder's radius, estimate the volume of the hollow cylinder.
If y=5^(x²-2x+1), then the slope at x = 2 is equal to
If y=5^(x²-2x+1), then the slope at x = 2 is equal to
Flashcards
Extrema on closed interval
Extrema on closed interval
For a continuous function on a closed interval, extrema (maxima or minima) can occur.
Second Derivative Test
Second Derivative Test
If f''(a) > 0 at a critical point, (a, f(a)) is a local minimum.
Exact Change in y
Exact Change in y
The exact change in y for a function is the difference f(x + Δx) - f(x).
Linear Approximation
Linear Approximation
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Rate of Change of Demand
Rate of Change of Demand
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Study Notes
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Answer to Question 1:
- The differential of y is not f(x)(Δx), thus that statement is not true
-
Answer to Question 2:
- If f(x) = 3sin(x/2) then the maxima and minima will have y coordinates with absolute value of 3 is true
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Answer to Question 3:
- If (a, f(a)) is a critical point and f''(a) > 0, then (a, f(a)) is a local minimum
-
Answer to Question 4:
- The estimated value of √4.4 using differentials is 2.1
-
Answer to Question 5
- The rate at which the volume of a cone is changing is given by dv/dt = (2πrh/3)(dr/dt) + (πr²/3)(dh/dt)
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Answer to Question 6:
- If a hollow cylinder is made by punching a concentric hole through a solid cylinder of radius = 5 cm and height = 10 cm. If the radius of the hole is 0.3cm less than the cylinder's radius, estimate the volume of the hollow cylinder ≈ 30π
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Answer to Question 7:
- If y = 5^(x^2-2x+1), then the slope at x=2 is equal to 10ln5
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