Download the App!

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

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Explain, in terms of linear approximations, why the approximation is reasonable.$\ln 1.05 \approx 0.05$

$L(0.05)=0.05($ accurate $)$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

Missouri State University

Oregon State University

Harvey Mudd College

University of Nottingham

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

01:42

Explain, in terms of linea…

02:27

01:22

01:36

$29-31$ Explain, in terms …

02:38

$$ \begin{array}{l}{29-31 …

00:56

00:30

00:38

01:32

00:34

this question assets took sprained by the approximation is reasonable. First off, where we have natural of one plus X, we're gonna be using a zero there for plugging zero. We know the natural log of one is simply zero. Now, to take the derivative we know the derivative of natural log of one plus X is 1/1 plus x. So 1/1 plus X is just if you put in 0 1/1 which simply want therefore l of acts is zero plus X minus A, which is X so l of 0.5 is simply gonna be 0.5

View More Answers From This Book

Find Another Textbook

01:10

Differentiate.$f(t)=\frac{2 t}{2+\sqrt{t}}$

03:01

$$\begin{array}{l}{\text { Foraging Many animals forage on resources tha…

01:35

Find an equation of the tangent line to the curve $y=x \sqrt{x}$ that is par…

01:47

Use logarithmic differentiation to find the derivative ofthe function.

01:21

Find the derivative of the function.$y=\cot ^{2}(\sin \theta)$

01:12

$9-12$ Sketch the graph of a function $f$ that is continuous on $[1,5]$ and …

02:00

Match the graph of each function in (a) (d) with the graph of its derivative…

05:33

Find the exact value of each expression.

(a) $$\ln (1 / e) (b) \log…

02:37

Find equations of the tangent line and normal line to thecurve at the gi…

01:14

Find the function $f$ such that $f ^ { \prime } ( x ) = f ( x ) [ 1 - f ( x …