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  • Please solve RD Sharma class 12 chapter Continuity exercise 8.2 question 3 subquestion (xi) maths textbook solution

Please solve RD Sharma class 12 chapter Continuity exercise 8.2 question 3 subquestion (xi) maths textbook solution

Answers (1)

Answer:

 x = 1

Hint:

 Check at end points.

Given:

 f(x)=\left\{\begin{array}{cc} 2 x & x<0 \\ 0 & 0 \leq x \leq 1 \\ 4 x & x>1 \end{array}\right.

Explanation:

At x = 0

\begin{aligned} &\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0} 2 x=2 \times 0=0-(1) \\ &\lim _{x \rightarrow 0^{+}} f(x)=\lim _{x \rightarrow 0} 0=0-(2) \\ &f(0)=0-(3) \end{aligned}

As (1)=(2)=(3)

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

At x = 1

\begin{aligned} &\lim _{x \rightarrow 1^{+}} f(x)=\lim _{x \rightarrow 1} 4 x=4 \times 1=4 \\ &f(1)=0 \end{aligned}

As

\lim _{x \rightarrow 1^{+}} f(x) \neq f(1)

Hence, f(X) is discontinuous at x = 1

Posted by

Gurleen Kaur

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