Evaluate lim x - 2 f x if it exists- where f x - matrix x-x- - x2lend matrix -right-

Lim_x → 2^ f(x)=lim_x → 2^ {x [x]} =lim_x → 2^ x lim_x → 2^ [x] =2 1=1 [∵lim_x → k^ [x]=k 1] lim_x → 2^+ f(x)=lim_x → 2^+(3x 5) =3(2) 5 =6 5 =1 Thus,lim_x → ...

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Byju's Answer

Standard XII

Mathematics

Limit

Evaluate lim ...

Question

Evaluate ${lim}_{x \to 2} f (x)$ (if it exists), where f(x)

$= ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x - [x], & x < 2 4, & x = 2 3 x - 5, & x > 2 \end{matrix}$

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Solution

${lim}_{x \to 2^{-}} f (x) = {lim}_{x \to 2^{-}} {x - [x]}$

$= {lim}_{x \to 2^{-}} x - {lim}_{x \to 2^{-}} [x]$

$= 2 - 1 = 1 [∵ {lim}_{x \to k^{-}} [x] = k - 1]$

${lim}_{x \to 2^{+}} f (x) = {lim}_{x \to 2^{+}} (3 x - 5)$

=3(2)-5

=6-5

=1

Thus, ${lim}_{x \to 2^{-}} f (x) = 1 = {lim}_{x \to 2^{+}} f (x)$

$\Rightarrow {lim}_{x \to 2} f (x) = 1$

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Similar questions

Q. Evaluate

\lim_{x \to 2} f (x)

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Find k so that ${lim}_{x \to 2}$ f(x) may exist, where $f (x) = {\begin{matrix} 2 x + 3, & x \leq 2 x + k, & x > 2 \end{matrix}$

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Let $f (x) = {\begin{matrix} x + 1, if x > 0 x - 1, if x < 0 \end{matrix}$ Prove that $l i m_{x \to 0}$ f(x)does not exist.

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Evaluate limx→2f(x) (if it exists), where f(x) =⎧⎪⎨⎪⎩x−[x],x<24,x=23x−5,x>2

limx→2−f(x)=limx→2−{x−[x]} =limx→2−x−limx→2−[x] =2−1=1[∵limx→k−[x]=k−1] limx→2+f(x)=limx→2+(3x−5) =3(2)-5 =6-5 =1 Thus,limx→2−f(x)=1=limx→2+f(x) ⇒limx→2f(x)=1

Evaluate ${lim}_{x \to 2} f (x)$ (if it exists), where f(x)

$= ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x - [x], & x < 2 4, & x = 2 3 x - 5, & x > 2 \end{matrix}$