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  • Find all points of discontinuity of f, where f x = sin x / x for x < 0 x + 1 for x > 0

23. Find all points of discontinuity of f, where 

f (x ) = \left\{\begin{matrix} \frac{\sin x }{x} & if x < 0 \\ x+1 & if x > 0 \end{matrix}\right.

Answers (1)

best_answer

Given function is
f (x ) = \left\{\begin{matrix} \frac{\sin x }{x} & if x < 0 \\ x+1 & if x > 0 \end{matrix}\right.
\lim_{x\rightarrow 0^-}f(x) = \lim_{x\rightarrow 0}\frac{\sin x}{x} = 1\\ \lim_{x\rightarrow 0^+}f(x) = x + 1 = 1\\ \lim_{x\rightarrow 0^-}f(x) = \lim_{x\rightarrow 0^+}f(x)
Hence, the function is continuous 
Therefore, no point of discontinuity
 

Posted by

Gautam harsolia

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