# ASU MAT 265 - mat265_test_2_review_2012_2 (5 pages)

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- Pages:
- 5
- School:
- Arizona State University
- Course:
- Mat 265 - Calculus for Engineers I

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MAT265 Review Problems for Exam 2 Product and Quotient Rules 1 Suppose 2 Suppose the derivative of with exists Assume that Find Let at a Find an equation of the tangent line to at b Find an equation of the tangent line to 3 Suppose tangent to at is and tangent to line tangent to the following curves at a at is Find the b Chain Rule using a table and 4 Let Using the table to compute the following derivatives a b c d e f 1 2 3 4 5 0 1 0 3 5 1 0 1 5 3 5 8 10 2 2 4 5 1 3 2 2 10 20 15 20 Derivative of composite functions 5 Suppose is differentiable on 2 2 with Evaluate the followings a b c Let Other Chain Rule 6 Solve a Suppose b If and and find Find when Horizontal tangent 7 Find all points on at which has horizontal tangent Tangent line using Implicit Differentiation 8 Find an equation of the tangent line to the curve at the given point a b c Second Derivatives 9 Find a b Related Rates 10 Sand falls from an overhead bin at a rate of 3 and accumulates in a cone shaped pile whose height is equal to twice the radius How fast is the height of the cone rising when the height is 2 meters 11 Two small planes approach an airport one flying due west at 120 mi hr and the other flying due north at 150 mi hr Assuming they fly at the same constant elevation how fast is the distance between the planes changing when the westbound plane is 180 mi from the airport and the northbound plane is 225 mi from the airport 12 If a snowball melts so that its surface area decreases at the rate of find the rate at which the diameter decreases when the diameter is 10 cm Hint Surface area 13 A 13 ft ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder away from the wall at a rate of How fast is the top of the ladder sliding down the wall when the foot of the ladder is 5 ft from the wall Linear Approximation 14 Use the linear approximation of the function at to approximate the number 15 Use Differentials or linear approximation to approximate the followings a b Calculating Error Using Differentials 16 The circumference of a sphere was measured to be 84 cm with a possible error in measurement of 0 2 cm a Use differentials to estimate the maximum error in the calculated surface area b Calculate the relative error c Calculate the percentage error Limits of Exponentials 17 Find the following limits a 18 Let a b b Find the following limits Inverse Functions 19 Consider a What is b Compute and let using the formula 20 Consider a Find b Find c Find for Derivatives of Natural Logarithms and Exponentials 21 Use logarithmic differentiation to find a b c 22 Suppose 23 Suppose if Find Hint Look at inverse function theorem in 3 2 What is What is Inverse Trigonometric Functions 24 Prove the followings a if then b if then c if then 25 Find l Hospital s Rule 26 Find the following limits using l Hospital s Rule a b c d e where k is an integer Note There is a reasonable assumption that most of these answers are not incorrect 1 40 2 a b 3 a b 4 a 100 b 100 c 16 d 60 e 120 5 a 3 b 0 6 a 21 2 7 c 3 b 33 8 a b 9 a 10 f 36000 b c meters per minute 11 mi hr distance between two planes is decreasing at a rate of 192mi hr 12 or decreasing at a rate of 13 the top of the ladder slides down the wall at 5 24 feet per second 14 15 a 0 05 b 4 02 16 a b 17 a 49 b 0 18 a 0 b 19 a b 20 a 0 21 a 22 23 c 0 48 b 2x cos x b c 1 c 24 25 26 a 1 2 b c 1 4 d e 3

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