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  • Explain solution RD Sharma class 12 chapter Continuity exercise 8.2 question 3 subquestion (x) maths

Explain solution RD Sharma class 12 chapter Continuity exercise 8.2 question 3 subquestion (x) maths

Answers (1)

Answer:

 x = 1

Hint:

 Check the continuity of function at end points.

Given:

 f(x)= \begin{cases}x^{10}-1 & x \leq 1 \\ x^{2} & x>1\end{cases}

Explanation:

At x = 1

\begin{aligned} &\lim _{x \rightarrow 1^{-}} x^{10}-1=\lim _{x \rightarrow 1} x^{10}-1 \\ &=(1)^{10}-1=1-1=0 \end{aligned}

\begin{aligned} &\lim _{x \rightarrow 1^{+}} f(x)=\lim _{x \rightarrow 1} x^{2} \\ &=(1)^{2}=1 \\ \end{aligned}

As

\begin{aligned} &\lim _{x \rightarrow 1^{-}} f(x) \neq \lim _{x \rightarrow 1^{+}} f(x) \end{aligned}

f(x) is not continuous at x = 1

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Gurleen Kaur

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