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  • Please solve RD Sharma class 12 chapter Continuity exercise 8.2 question 1 maths textbook solution

Please solve RD Sharma class 12 chapter Continuity exercise 8.2 question 1 maths textbook solution

Answers (1)

Answer:

f(x) is everywhere continuous.

Hint:

 A function is everywhere continuous when it is continuous at every x \in IR

Given:

 f(x)=\left\{\begin{array}{cc} \frac{\sin x}{x} & x<0 \\ x+1 & x \geq 0 \end{array}\right.

Explanation:

Now, at x = 0

\begin{aligned} &\lim _{x \rightarrow 0^{-}} f(x)=\lim _{h \rightarrow 0} \frac{\sin x}{x} \quad\left[\because \lim _{h \rightarrow 0} \frac{\sin x}{x}=1\right] \\ &=1 \\ &\lim _{x \rightarrow 0^{+}} f(x)=\lim _{h \rightarrow 0} x+1=1 \end{aligned}

And

f(x) = 0 + 1 = 1

As,

\left.\lim _{x \rightarrow 0} f(x)=f(0) \quad \text { [for continuity } \lim _{x \rightarrow 0} f(x)=f(0)\right]

Hence, f(x) is everywhere continuous.

Note: sine function, identity function, polynomial functions are everywhere continuous.

Posted by

Gurleen Kaur

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