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  • Please solve RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 1 maths textbook solution

Please solve RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 1 maths textbook solution

Answers (1)

Answer:

 The correct option is (c)

Hint:

 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)=\frac{4-x^{2}}{4 x-x^{3}}

Solution:

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

\begin{aligned} &\lim _{x \rightarrow a} f(x)=f(a) \\ &f(x)=\frac{4-x^{2}}{4 x-x^{3}} \\ &f(x)=\frac{4-x^{2}}{x\left(4-x^{2}\right)} \\ &f(x)=\frac{1}{x} \\ &\text { Where } x \neq 0, \pm 2 \end{aligned}

f(x) is continuous for all real numbers except (0, \pm2).

Therefore, it is continuous exactly at three points (0, \pm2)

So, the correct option is (c)

Posted by

Gurleen Kaur

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