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Use a linear approximation to estimate the given number.$e^{-0.015}$

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$L(0.015)=1-1(0.015)=0.985$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

Missouri State University

Oregon State University

Harvey Mudd College

Baylor University

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.

02:03

Use a linear approximation…

00:27

02:54

01:02

in this problem. We are us usually immunization to approximate each of the negative for 0 15 So we're gonna start off a solution by defining function it. We're going to say that our function is aegypti fest and we're gonna by the legalization of their function one x is you know, So let's remember impressionable the immunization of a function that point next. No physical, too functional legs at that boring extra. Plus, they would want a functional later. That point most Bye bye X minus. So let's see. We like to function at excellent. Extending this case is yourself when x zero is you 20 which is long. Let's do the same for today would talk dysfunction that primal exists. You two ex since our orginally muscle function is either the exit from this inevitable dysfunction at X zero is zero. So this is one. So we're just gonna plug these values into the the musician equation and front of the musician function to be worn plus foreign. Explain its hero sort of the equation while immunization is one of us. Yes. Okay, next we are trying Thio folks made e to the negative point. So in This guy's ex is negative point team. So we just stopped like this Ice who to this re musician? Your questions So which will be born minus point or if I so the approximation this number will be 0.98

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