Name: ______Period: ____
Calculus AB AP
Review: Linear Approximation
1. The volume of a cylindrical tin can with a top and a bottom is to be cubic inches. If a minimum amount of tin is to be used to construct the can, what must be the height, in inches, of the can?
A. B. C. D. 4* E. 8
2. Consider all right circular cylinders for which the sum of height and circumference is 30 centimeters. What is the radius of the one with maximum volume?
A. 3 cm B. 10 cm C. 20 cm D. cm E. cm*
3. For small values of h, the function is best approximated by which of the following?
A. B. * C. D. E.
4. Let . Approximate the value of using the tangent line to f at .
5. Let f be a differentiable function such that and . If the tangent line to the graph of f at is used to find an approximation to a zero of f , find that approximation.
tangent line: , zero:
6. If Newton’s method is used to approximate a zero of the function , and is used as an initial approximation. Find the fourth approximation.
()
7. Find an expression for dy for each of the following functions.
(a).
(b).
(c).
8. Use differentials to approximate the following. Leave answers in exact form, i.e. radicals and .
(a).
(b). 9.7
(c). , –6
9. A concrete pipe 4 inches thick needs to be constructed with a length of 12 feet and an inner radius of 2 feet. Use differentials to approximate the amount of concrete needed.
[Note: h is a constant, which is 12 feet]
ft3
10. Use Newton’s Method to approximate by following the steps listed below:
(a) Construct a function that has a zero of .
(b) Use Newton’s Method to approximate to three decimal places using for initial guess. Show setup below and record your answer after each iteration in the table.
/ 9.7
/ 9.695
/ 9.695 [stop here]
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