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  • Please solve RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 9 maths textbook solution

Please solve RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 9 maths textbook solution

Answers (1)

Answer:

 The correct option is (b)

Hint:

 Use the given formula:

(i) A function f(x) is said to be continuous at a point x = a of its domain, if

\lim _{x \rightarrow a^{+}} f(a+h)=\lim _{x \rightarrow a^{-}} f(a-h)=f(a)

Given:

 f(x)=\left\{\begin{array}{l} \frac{e^{1 / x}-1}{e^{1 / x}+1} \\ 0 \end{array}\right.  \begin{aligned} , x & \neq 0 \\ , x &=0 \end{aligned}

Solution:

Using substitution method,

\text { Let } e^{1 / x}=t \text { so, } x \rightarrow 0, t \rightarrow \infty

\begin{aligned} &\lim _{t \rightarrow \infty} f(x)=\lim _{t \rightarrow \infty}\left(\frac{t-1}{t+1}\right) \\ &=\frac{1-0}{1+0}=1 \quad \quad[L-\text { Hospital rule }] \end{aligned}

And,

\begin{aligned} &f(0)=0 \\ &\text { Therefore, } \lim _{x \rightarrow 0} f(x) \neq f(0) \end{aligned}

Hence, f(x) is discontinuous at x = 0

So, option (b) is correct.

Posted by

Gurleen Kaur

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