if-f-x-x-x-g-x-x-2-1-find-lim-x-1-f-g-x-

Question Number 68885 by aliesam last updated on 16/Sep/19

i f

f (x) = \frac{∣ x ∣}{x}

g (x) = x^{2} - 1

f i n d

\underset{x \to 1}{l i m} f (g (x))

Commented by kaivan.ahmadi last updated on 16/Sep/19

f (g (x)) = f (x^{2} - 1) = \frac{∣ x^{2} - 1 ∣}{x^{2} - 1}

{l i m}_{x \to 1^{+}} \frac{∣ x^{2} - 1 ∣}{x^{2} - 1} = {l i m}_{x \to 1^{+}} \frac{x^{2} - 1}{x^{2} - 1} = 1

{l i m}_{x \to 1^{-}} \frac{∣ x^{2} - 1 ∣}{x^{2} - 1} = {l i m}_{x \to 1^{-}} \frac{- (x^{2} - 1)}{x^{2} - 1} = - 1

\Rightarrow {l i m}_{x \to 1} f (g (x)) i s n o t e x i s t .

Commented by aliesam last updated on 16/Sep/19

i f

\underset{x \to c}{l i m} g (x)

t h e n

\underset{x \to c}{l i m} f (g (x))

= f (\underset{x \to c}{l i m} g (x))

= f (b)

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