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(5) Compute the following limits directly, without using tables or graphs.. Sh 1 1 (x+h)² x² h (a) lim h→0

(5) Compute the following limits directly, without using tables or graphs.. Sh 1 1 (x+h)² x² h (a) lim h→0

Calculus: Early Transcendentals
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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(5) Compute the following limits directly, without using tables or graphs.. 1 1 (x+h)²x² h (a) lim h→0 -
Transcribed Image Text:(5) Compute the following limits directly, without using tables or graphs.. 1 1 (x+h)²x² h (a) lim h→0 -
(3) Sketch the graph of the function and use it to determine all values of a for which lim f(x) does not exist. x→a 2x-4 if x>1 f(x)=x²-3 if -2<x<1 |x if x < -2 -6 -5 -4 (4) Suppose you were trying to prove that limx³ = 1 x→l 2+ -3 0 -2 Does this value of satisfy the definition for the given &? f not, compute a value of that would work. -1 5 4 3 2 -1- 0 -1- --2 -3 --4- 1 2 The graph below depicts ƒ(x)=x³ with ε = 0.2 and 8=0.2 (where & and 8 are as described in the definition of limit). (Note: you should be able to recreate such a graph by hand if given f(x),a,ɛ, on the exam) Show thought process. tat 3 2 4 5
Transcribed Image Text:(3) Sketch the graph of the function and use it to determine all values of a for which lim f(x) does not exist. x→a 2x-4 if x>1 f(x)=x²-3 if -2<x<1 |x if x < -2 -6 -5 -4 (4) Suppose you were trying to prove that limx³ = 1 x→l 2+ -3 0 -2 Does this value of satisfy the definition for the given &? f not, compute a value of that would work. -1 5 4 3 2 -1- 0 -1- --2 -3 --4- 1 2 The graph below depicts ƒ(x)=x³ with ε = 0.2 and 8=0.2 (where & and 8 are as described in the definition of limit). (Note: you should be able to recreate such a graph by hand if given f(x),a,ɛ, on the exam) Show thought process. tat 3 2 4 5
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