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Consider the function f(x) = 3 + \int^{1+x^2}_2 5/2(1 + t^2) dt. (a) Find the linearization of...

Question:

Consider the function f(x) = 3 +{eq}\int^{1+x^2}_2 5/2(1 + t^2) {/eq} dt.

(a) Find the linearization of f(x) at a = 1.

(b) Use the linearization in (a) to approximate {eq}\int^{1+(1.1)^2}_2 5/2(1 + t^2) {/eq}dt.

Linearization:

When functions are extremely difficult to evaluate, the process of linearization helps us approximate the value of the function. The formula to perform linearization is given as {eq}f(x) = f(x_0) + h \cdot f'(x_{0}) {/eq}, where {eq}f(x)_0 {/eq}, {eq}h = x - x_0 {/eq}, and {eq}f'(x_{0}) {/eq}, are provided in order to find the {eq}f(x) {/eq} value.

Answer and Explanation:

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Given: {eq}f(x) = 3+\int^{1+x^2}_2 \frac{5}{2}(1+t^2) dt {/eq}:


a. The point of reference will be at {eq}x = a = 1 {/eq}:


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Linearization of Functions

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Chapter 10 / Lesson 1
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