- #1
misterau
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Homework Statement
Let the function f be given by f (x) = x^2
(a) Determine the tangent line to the graph of f at x = 1. Denote this by y = g (x) .
(b) Let [tex]\epsilon[/tex] be a positive number. Solve the inequality|f (x) - g (x)| <[tex]\epsilon[/tex]
(c) What does part b) tell us about the accuracy of the tangent-line approximation to f ?
Illustrate your answer by using the values [tex]\epsilon[/tex] = 0.01 and [tex]\epsilon[/tex] = 0.0001.
Homework Equations
The Attempt at a Solution
(a) For y = mx + b
f'(x) = 2*x
f'(1) = 2*1 = 2
b =1 -2(1)
= -1
g(x) = 2x -1
(b) This where I am having problems
|f (x) - g (x)| = | x^2 -2*x +1| = |(x-1)(x-1)|
so
|(x-1)(x-1)|<[tex]\epsilon[/tex]
|(x-1)(x-1)|<K|(x-1)|<[tex]\epsilon[/tex]
assuming |x-1|<K
Then I realized I can not make this assumption..
I am not sure what I can assume to get: |x-1| < ([tex]\epsilon[/tex]/k)
Now do I get rid of the other |x-1|?
Basically confused, I find these Definition of limits Q's difficult.