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Question
Find a linear approximation for the following functions at the indicated points.
h(x) = `x/(x + 1), x_0` = 1
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Solution
h(x0) = h((1)
= `1/(1 + 1)`
= `1/2`
h'(x) `((x + 1) xx 1 - x xx 1)/(x + 1)^2`
= `(x + 1 - x)/(x + 1)^2`
= `1/(x + 1)^2`
h'(x0) = h'(1) = `1/4`
L(x) = h(x0) + h'(x0)(x – x0)
= `1/2 + 1/4 (x - 1)`
= `(2 + x - 1)/4`
= `(x + 1)/4`
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