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Find Functions and Evaluate Limits

1. Find functions f and g such that

f(x) = (f.g)(x) where f(x) = (x^2+1)^0.205

2. Evaluate lim

lim f(x) = -x^2+1 x< = -1
x-> -1 f(x) = 2x^2+3x x > -1

Solution Preview

(2) we compute the one-sided limits as follows:

as x approaches - 1 from the left, x< -1, so lim_{ x -> - 1 left} (-x^2 + 1) = (-1)^2 ...

Solution Summary

Limits are evaluated and functions are found.

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