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$7-10$ Verify the given linear approximation at $a=0 .$ Thendetermine the values of $x$ for which the linear approximation is$\tan x \approx x$

$L(x)=0+(x-a)=x$For accuracy $y=0.1$ then $x$ must be $-0.6176< x <0.6176$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

Missouri State University

Campbell University

Idaho State 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.

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$7-10$ Verify the given li…

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Verify the given linear ap…

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in this trouble were given a function which is a first for us to determine. Finally, immunization. It's like underestimate. Erm devalues our bikes for Ridge, the legalization is that correct? Within point, Let's start with Finding dude are functioning at crime affects its secret. I'm scared of heights. So selective function And then there were two at the given 20.0 would be zero. And if prime of zero would be on, let's find the legalization function that would be a zero plus that prime zero times X minus zero. And if you plug gaps, you on a friend, you're here. We plan is to be, um, so an agent Eggs? Yes. Now what can afford Excellent for which the musicians that fun. So basically we're working for that's seen it, you tell it. So if you sold this inequality, we determined the xB between pouring 63 and negative forces as long as accident. This untold this approximation is that group within 0.1

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