Fx - x - if x- 1 5- if x - 1Check whether fx is continuous at x-0- x- 1- x-2-

at #10;x=0 f(0)=0 LHL=lim_h→0f(0 h) =lim_h→0 h=0 RHL=lim_h→0f(0+h) =lim_h→0h=0 ∴>continuous >at x=0 at #10;x=1 f( ...

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Continuity of a Function

fx = x , if x...

Question

$f (x) = x, i f x \leq 1$
$5, i f x \geq 1$
Check whether $f (x)$ is continuous at $x = 0 ? x = 1 ? x = 2 ?$

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Solution

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Similar questions

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} (1 + a x)^{\frac{1}{x}}, if x < 0 b, if x = 0 \frac{(x + c)^{\frac{1}{3}} - 1}{(x + 1)^{\frac{1}{2}} - 1}, if x > 0 \end{matrix}

x = 0

f (x) =

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

f

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

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