For what value of - is the function defined by fx- -x2-2 x- if x - 0- 4 x-1- if x-0 -continuous at x-0 - What about continuity at x-1 -

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For what valu...

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For what value of is the function defined by

continuous at x = 0? What about continuity at x = 1?

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⎧ ⎨ ⎩ \begin{matrix} 2 x, i f x < 0 0, i f 0 \leq x \leq 1 4 x, i f x > 1 \end{matrix}

f

f (x) =

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

x = 0

x = 1

x = 2

Is the function f defined by

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

λ

f (x) = {\begin{matrix} λ (x^{2} - 2 x), if x \leq 0 4 x + 1, if x > 0 \end{matrix}

x = 0

x = 1

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

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