Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Use the definition of derivative to prove that

$ \displaystyle \lim_{x \to 0} \frac {\ln (1 + x)}{x} = 1 $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Doruk Isik

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

01:18

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 6

Derivatives of Logarithmic Functions

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

03:30

Use the definition of the …

02:07

Show that $\lim _{x \right…

02:16

Differentiate $\ln x,$ for…

02:14

Show that $$\lim _{x \righ…

00:39

Calculate the derivative w…

05:13

Use graphical differentiat…

02:12

Find the derivative of the…

he's trouble. We rest used definition of spirited Program Limited's except watch your nature longer. One plus X divided by accident or less shirt. What's Remember deformation? Oh, there will be no limit is exposed to zero Equifax writing staff of zero You like my ex one syrup would be f from X b o From Ms Devane terms. If you could define a function of a Pakistan, we would be able to find charity off a function. But say that every pegs is they go to natural law on us. Thanks. And one set of because limit as except for zero mention logo minus. Now we're in Cassidy fo zero. If this is a zero would be natural for zero. There we are natural longer Po po zero divided by X minus. There would then be equal to a crime off X where prime affects is just one or were born plus X here we know that natural love one is a zero and this is what we're intransigent. All we need to do you still have laid a form of backs on ecstasy zero that is on over one month ago. There is one more that is equal for and that is what has given into problems

View More Answers From This Book

Find Another Textbook

Oregon State University

Baylor University

University of Nottingham