I. Define the function [In(r+ 1)] cosh r + tanr ,r20 (sinh r) sec- (r – 2) S(x) = ,z <0 1. Show that f is continuous at r = 0. 2. Is f differentiable at z = 0? Justify your answer. П. Find dy There is no need to simplify. d.r cos- (sin r) – sech(tan-r) 1. y = ecosh z 4r* (log, a) 2. y = (csc" r)Vsinh(2r – 8 III. Find dy using implicit differentiation. dr sec (ry?) = (cosh r)(tanh =+v5) + 2 csc-" (tan(y + 1)) It.

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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I. Define the function
f(x) = ! In(x + 1)] cosh r + tan r ,r>0
|(sinh r) sec- (r – 2)
,I < 0
1. Show that f is continuous at r = 0.
2. Is f differentiable at a = 0? Justify your answer.
dy
There is no need to simplify.
dr
II. Find
cos- (sin a) – sech(tan-!a)
1. y =
ecosh z
4r (loga r)"
(csc r) sinh(2r – 8)
2. y =
III. Find
fip
using implicit differentiation.
dr
sec (ry*) = (cosh a)(tanh +v) + 2 csc- (tan(y + 1))
Transcribed Image Text:I. Define the function f(x) = ! In(x + 1)] cosh r + tan r ,r>0 |(sinh r) sec- (r – 2) ,I < 0 1. Show that f is continuous at r = 0. 2. Is f differentiable at a = 0? Justify your answer. dy There is no need to simplify. dr II. Find cos- (sin a) – sech(tan-!a) 1. y = ecosh z 4r (loga r)" (csc r) sinh(2r – 8) 2. y = III. Find fip using implicit differentiation. dr sec (ry*) = (cosh a)(tanh +v) + 2 csc- (tan(y + 1))
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