If f x - x -2- thenA- lim x - 2- f x -lim x - 2- f x B- lim x - 2- f x -0C- lim x - 2- f x -0D- f x is continuous at x -2

The correct option is D f (x) is continuous at x = 2Here f(2) = 0 lim_x → 2 f(x)= lim_k → 0f(2 h)=lim_k → 0|2 h 2|=0 lim_x → 2+f(x)= lim_k → 0f(2+h)=lim_k ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Derivatives

If f x =| x -...

Question

If f(x) = $| x - 2 |$ , then

{lim}_{x \to 2 +} f (x) \neq 0

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{lim}_{x \to 2 -} f (x) \neq 0

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{lim}_{x \to 2 +} f (x) \neq {lim}_{x \to 2 -} f (x)

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f (x) i s c o n t i n u o u s a t x = 2

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Solution

The correct option is D $f (x) i s c o n t i n u o u s a t x = 2$
Here f(2) = 0
${lim}_{x \to 2 -} f (x) = {lim}_{k \to 0} f (2 - h) = {lim}_{k \to 0} | 2 - h - 2 | = 0$
${lim}_{x \to 2 +} f (x) = {lim}_{k \to 0} f (2 + h) = {lim}_{k \to 0} | 2 + h - 2 | = 0$
Hence it is continuous at x = 2

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If f(x) = |x−2|, then

The correct option is D f(x) is continuous at x=2Here f(2) = 0 limx→2−f(x)=limk→0f(2−h)=limk→0|2−h−2|=0 limx→2+f(x)=limk→0f(2+h)=limk→0|2+h−2|=0 Hence it is continuous at x = 2

If f(x) = $| x - 2 |$ , then

The correct option is D $f (x) i s c o n t i n u o u s a t x = 2$
Here f(2) = 0
${lim}_{x \to 2 -} f (x) = {lim}_{k \to 0} f (2 - h) = {lim}_{k \to 0} | 2 - h - 2 | = 0$
${lim}_{x \to 2 +} f (x) = {lim}_{k \to 0} f (2 + h) = {lim}_{k \to 0} | 2 + h - 2 | = 0$
Hence it is continuous at x = 2