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  • Need solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 3 subquestion (v)

Need solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 3 subquestion (v)

Answers (1)

Answer:

 x = 0

Hint:

 \lim _{x \rightarrow a} f(x)+g(x)=\lim _{x \rightarrow a} f(x)+\lim _{x \rightarrow a} g(x)

Given:

 f(x)= \begin{cases}\frac{\sin x}{x}+\cos x & x \neq 0 \\ 5 & x=0\end{cases}

Explanation:

At x = 0

\begin{aligned} &\text { L.H. } L=\lim _{x \rightarrow 0^{-}} f(x)=\lim _{h \rightarrow 0}(0-h)=\lim _{h \rightarrow 0} \frac{\sin (-h)+\cos (-h)}{-h} \\ &=\lim _{h \rightarrow 0} \frac{-\sinh }{-h}+\cosh =1+1=2 \end{aligned}

\begin{aligned} &R . H \cdot L=\lim _{x \rightarrow 0^{+}} f(x)=\lim _{h \rightarrow 0}(0+h)=\lim _{h \rightarrow 0} \frac{\sinh }{h}+\cosh =1+1=2 \\ &\text { Also } f(0)=5 \\ &\text { Thus } L . H . L=R . H . L \neq \mathrm{f}(0) \end{aligned}

As

\lim _{x \rightarrow 0} f \rightarrow(x) \neq x f(0)

f is not continuous at x = 0

Posted by

Gurleen Kaur

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