Is the function f defined by fx- x- if x - 1- 5- if x-1 -continuous at x-0 - At x-1 - At x-2 -

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

Is the functi...

Question

Is the function f defined by

continuous at x = 0? At x = 1? At x = 2?

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f

f (x) =

{\begin{matrix} x, i f x \leq 1 5, i f x > 1 \end{matrix}

x = 0

x = 1

x = 2

f

f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \frac{{cos}^{2} x - {sin}^{2} x - 1}{\sqrt{x + 1} - 1} & , if x \neq 0 k & , if x = 0 \end{matrix},

x \neq 0,

x = 0

f

f (x) = {\begin{matrix} x + 2, i f x \leq 1 x - 2, i f x > 1 \end{matrix}

f (x) = {\begin{matrix} x^{2} sin \frac{1}{x}, & i f x \neq 0 0, & i f x = 0 \end{matrix}

f,

f

f (x) = ⎧ ⎨ ⎩ \begin{matrix} - 2, i f x \leq - 1 2 x, i f - 1 \leq x \leq 1 2, i f x > 1 \end{matrix}

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