Explanation Given: The function is lim h → 0 g ( h ) = L . Formula used: The limit law is lim x → c x = c . The power law: If lim x → c f ( x ) and lim x → c g ( x ) both exists, then lim x → c ( f ( x ) ) n = ( lim x → c f ( x ) ) n Calculation: Part a: The function is lim h → 0 g ( h ) = L . We have to prove that lim h → 0 g ( a h ) = L . As you know that h → 0 so a h → 0 Let v = a h . Now, find the value of function. lim h → 0 g ( a h ) = lim h → 0 g ( w ) = L Hence, lim h → 0 g ( a h ) = L . Part b: The function is lim h → 1 g ( h ) = L

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 2.3, Problem 45E

To determine

a. Explain why limh→0g(ah)=L for any constant a≠0.

b. Assume that limh→1g(h)=L, is it still necessarily true that limh→1g(ah)=L ?

c. Illustrate (a) and (b) with the function f(x)=x2.

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Chapter 2.3, Problem 44E

Chapter 2.3, Problem 46E

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Chapter 2 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E

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a. Explain why lim h → 0 g ( a h ) = L for any constant a ≠ 0 . b. Assume that lim h → 1 g ( h ) = L , is it still necessarily true that lim h → 1 g ( a h ) = L ? c. Illustrate (a) and (b) with the function f ( x ) = x 2 .

Solution Summary: The author explains how to determine why undersethto 0mathrmlimg(ah-)=L for any constant.

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a. Explain why limh→0g(ah)=L for any constant a≠0.

b. Assume that limh→1g(h)=L, is it still necessarily true that limh→1g(ah)=L ?

c. Illustrate (a) and (b) with the function f(x)=x2.

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Chapter 2 Solutions

a. Explain why lim h → 0 g ( a h ) = L for any constant a ≠ 0 . b. Assume that lim h → 1 g ( h ) = L , is it still necessarily true that lim h → 1 g ( a h ) = L ? c. Illustrate (a) and (b) with the function f ( x ) = x 2 .

Solution Summary: The author explains how to determine why undersethto 0mathrmlimg(ah-)=L for any constant.

Concept explainers

Videos

a. Explain why limh→0g(ah)=L for any constant a≠0. b. Assume that limh→1g(h)=L, is it still necessarily true that limh→1g(ah)=L ? c. Illustrate (a) and (b) with the function f(x)=x2.

Want to see the full answer?

Chapter 2 Solutions

a. Explain why limh→0g(ah)=L for any constant a≠0.

b. Assume that limh→1g(h)=L, is it still necessarily true that limh→1g(ah)=L ?

c. Illustrate (a) and (b) with the function f(x)=x2.