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What is the area of the line 2^x using linear approximation.

Question:

What is the area of the line {eq}2^x {/eq} using linear approximation.

Linearization and Area:

Let us suppose that any function {eq}y=f(x) {/eq} of one variable is given.

Then the Linearization of {eq}y=f(x) {/eq} with respect to any point {eq}x=a {/eq} is given by:

{eq}L(x) = f(a) + \left( {x - a} \right)f'(a) {/eq}

Answer and Explanation:

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In this case, the given function is:{eq}f(x) ={2^x}, \; a = 0. {/eq}

Here:

{eq}\displaystyle f(x) ={2^x}\Rightarrow f\left(0\right) = 1...

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Linearization of Functions

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Chapter 10 / Lesson 1
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