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

Evaluate lim ...

Question

Evaluatef(x), where f(x) =

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Solution

The given function is

f(x) =

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Findf(x), where f(x) =

lim x \to 0 f (x),

f (x) = ⎧ ⎨ ⎩ \begin{matrix} \frac{| x |}{x}, & x \neq 0 0, & x = 0 \end{matrix}

\lim_{x \to 0} f (x)

f (x) = \{\begin{cases} \frac{|x|}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases}

f (x) = \begin{matrix} \frac{sin [x]}{[x]}, & [x] \neq 0 0 & [x] = 0 \end{matrix}

[.]

denotes the greatest integer function.,then

lim x \to 0 f (x)

lim x \to 0 f (x),

{\begin{matrix} \frac{x}{| x |}, & x \neq 0 0, & x = 0 \end{matrix}

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

Standard XII Mathematics

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