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Piecewise Functions, Derivatives and Limits

1. A piecewise function is given. Use the function to find the indicated limits, or state that a limit does not exist.

(a) lim is over x gd - f(x), (b) lim is over x gd + f(x), and (c) lim is over xgd f(x)

f(x) = { x^2 - 5 if x < 0 }
{ -2 if x >= 0 } : d = -3

(a) -5 (b) -2 (c) does not exist
(a) 4 (b) 4 (c) 4
(a) -2 (b) -5 (c) does not exist
(a) -5 (b) -2 (c) -2

2. Find the derivative of f of x
f(x) = x^3 + 19 : x = 8

The third question I've attached.

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Piecewise Functions, Derivatives and Limits are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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