Explanation Given information: The expression is 1 2 b . Explanation: As b increases, b also increases Hence, as b increases,

Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version

14th Edition

ISBN: 9780134463230

Author: Larry J. Goldstein, David I Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 9.6, Problem 6E

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Whether the expression 12b approaches a limit as b→ ∞, or not; if so, find the limit

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Chapter 9.6, Problem 5E

Chapter 9.6, Problem 7E

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A ladder 25 feet long is leaning against the wall of a building. Initially, the foot of the ladder is 7 feet from the wall. The foot of the ladder begins to slide at a rate of 2 ft/sec, causing the top of the ladder to slide down the wall. The location of the foot of the ladder, its x coordinate, at time t seconds is given by x(t)=7+2t. wall y(1) 25 ft. ladder x(1) ground (a) Find the formula for the location of the top of the ladder, the y coordinate, as a function of time t. The formula for y(t)= √ 25² - (7+2t)² (b) The domain of t values for y(t) ranges from 0 (c) Calculate the average velocity of the top of the ladder on each of these time intervals (correct to three decimal places): . (Put your cursor in the box, click and a palette will come up to help you enter your symbolic answer.) time interval ave velocity [0,2] -0.766 [6,8] -3.225 time interval ave velocity -1.224 -9.798 [2,4] [8,9] (d) Find a time interval [a,9] so that the average velocity of the top of the ladder on this…

Total marks 15 3. (i) Let FRN Rm be a mapping and x = RN is a given point. Which of the following statements are true? Construct counterex- amples for any that are false. (a) If F is continuous at x then F is differentiable at x. (b) If F is differentiable at x then F is continuous at x. If F is differentiable at x then F has all 1st order partial (c) derivatives at x. (d) If all 1st order partial derivatives of F exist and are con- tinuous on RN then F is differentiable at x. [5 Marks] (ii) Let mappings F= (F1, F2) R³ → R² and G=(G1, G2) R² → R² : be defined by F₁ (x1, x2, x3) = x1 + x², G1(1, 2) = 31, F2(x1, x2, x3) = x² + x3, G2(1, 2)=sin(1+ y2). By using the chain rule, calculate the Jacobian matrix of the mapping GoF R3 R², i.e., JGoF(x1, x2, x3). What is JGOF(0, 0, 0)? (iii) [7 Marks] Give reasons why the mapping Go F is differentiable at (0, 0, 0) R³ and determine the derivative matrix D(GF)(0, 0, 0). [3 Marks]

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Chapter 9 Solutions

Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version

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Whether the expression 1 2 b approaches a limit as b → ∞ , or not; if so, find the limit

Solution Summary: The author analyzes how the expression 12sqrtb approaches a limit as b to.

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Whether the expression 12b approaches a limit as b→ ∞, or not; if so, find the limit

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Chapter 9 Solutions