1. The linear approximation at x=0 to f(x) = 1 / √8-x is L(x) = A+Bx where  A = ?  B = ?

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Hi there! I have a couple of questions about some calculus problems I am working on. I was hoping someone could help me and show their work since I actually want to learn this. I will be upvoting all correct answers. I really appreciate any help you can provide.

 

1. The linear approximation at x=0 to f(x) = 1 / √8-x is L(x) = A+Bx where 

A = ? 

B = ? 

 

2. Use linear approximation, i.e. the tangent line, to approximate √25.1 as follows:

let f(x) = √x

The equation of the tangent line in slope-intercept form to f(x) at x=25 can be written in the form y=mx+b where: 

m = ?

b = ?

Using this we find our approximation for √25.1 is ?

For the last part, give your answer to at least 6 sig figs or use fractions to give the exact answer.

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