Question 1 Given (i) e² (a) find y' e2y + x = y (ii) xy + y² = 1 (b) find y" Question 2 Answer the questions below: (a) Let f(x) = x, choose an appropriate center to approximate 64.1. (b) Let f(x)=3xe 2x-10. Find the linear approximation to f(x) at x = 5 and use it to approx- imate f(5.1) Question 3 Find a formula for f(n) (x). Clearly, specify the least value n can be. (a) f(x) = apx+q (b) f(x)=(ax+1)e¯ (c) [optional] Let g(x) = sin x show that 9(n) (x) repeats in sets of 4. That is, there are only 4 different n-th derivatives depending on the value of n.

Question 1 Given (i) e² (a) find y' e2y + x = y (ii) xy + y² = 1 (b) find y" Question 2 Answer the questions below: (a) Let f(x) = x, choose an appropriate center to approximate 64.1. (b) Let f(x)=3xe 2x-10. Find the linear approximation to f(x) at x = 5 and use it to approx- imate f(5.1) Question 3 Find a formula for f(n) (x). Clearly, specify the least value n can be. (a) f(x) = apx+q (b) f(x)=(ax+1)e¯ (c) [optional] Let g(x) = sin x show that 9(n) (x) repeats in sets of 4. That is, there are only 4 different n-th derivatives depending on the value of n.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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