Check the continuity of -f- given by f x -left matrix 4- x - 2 -if - x leq 0 1x -5 -if - 0- x leq 14 x- 2-9 - if - 1 e qlend matrix -right- at points x -0-1-2 formA- undefinedB- undefinedC- undefinedD- undefined

at x = 0 f(0) = 4 (0)^2 = 4 lim_x → 0 =4 x^2 = 4 0^2 =4 lim_x → 0^ = x 5 =0 5 = 5 Since f(0) =lim_x → 0^ ≠lim_x → 0^tf(x) f(x) is not continous at x = 0. ...

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Check the con...

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Check the continuity of 'f' given by
$f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 4 - x^{2} & i f & x \leq 0 x - 5 & i f & 0 < x \leq 1 4 x^{2} - 9 & i f & 1 < x < 2 3 x + 4 & i f & x >\geq 2 \end{matrix}$ at points x = 0, 1, 2 form

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Solution

at x = 0
f(0) = $4 - (0)^{2}$ = 4
${lim}_{x \to 0} = 4 - x^{2} = 4 - 0^{2} = 4 {lim}_{x \to 0^{-}} = x - 5 = 0 - 5 = - 5 S i n c e f (0) = {lim}_{x \to 0^{-}} \neq {lim}_{x \to 0^{t}} f (x)$
f(x) is not continous at x = 0.

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Check the continuity of 'f' given by f(x)=⎧⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪⎩4−x2ifx≤0x−5if0<x≤14x2−9if1<x<23x+4ifx>≥2 at points x = 0, 1, 2 form

at x = 0 f(0) = 4−(0)2 = 4 limx→0=4−x2=4−02=4limx→0−=x−5=0−5=−5Since f(0)=limx→0−≠limx→0tf(x) f(x) is not continous at x = 0.

Check the continuity of 'f' given by
$f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 4 - x^{2} & i f & x \leq 0 x - 5 & i f & 0 < x \leq 1 4 x^{2} - 9 & i f & 1 < x < 2 3 x + 4 & i f & x >\geq 2 \end{matrix}$ at points x = 0, 1, 2 form

at x = 0
f(0) = $4 - (0)^{2}$ = 4
${lim}_{x \to 0} = 4 - x^{2} = 4 - 0^{2} = 4 {lim}_{x \to 0^{-}} = x - 5 = 0 - 5 = - 5 S i n c e f (0) = {lim}_{x \to 0^{-}} \neq {lim}_{x \to 0^{t}} f (x)$
f(x) is not continous at x = 0.