If fx- -x-1- x0 -For what value s of a does lim x - a fx exists-

The given function is When a lt; 0, When a gt; 0 Thus, exists for all a ≠ 0. ...

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Necessary Condition for an Extrema(Is a Function Differentiable at Boundaries)

If fx=[ |x|+1...

Question

If f(x) =.

For what value (s) of a does f(x) exists?

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f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} | x | + 1, & x < 0 0, & x = 0 | x | - 1, & x > 0 \end{matrix}

a

lim x \to a f (x)

f (x) =

⎧ ⎨ ⎩ \begin{matrix} | x | + 1, & x < 0 0, & x = 0 x^{3} | x | - 1 & x > 0 \end{matrix}

lim x \to a f (x)

Evaluatef(x), where f(x) =

f (x) ⎧ ⎨ ⎩ \begin{matrix} m x^{2} + n, x < 0 n x + m, 0 \leq x \leq n x^{3} + m, x > 1 \end{matrix} 1

m

n

lim x \to 0 f (x)

lim x \to 1 f (x)

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