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  • Need solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 3 subquestion (ix)

Need solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 3 subquestion (ix)

Answers (1)

Answer:

 at x = 3

Hint:

 Check the continuity of function at breaking points.

Given:

 f(x)=\left\{\begin{array}{cc} |x|+3 & x \leq-3 \\ -2 x & -3<x<3 \\ 6 x+2 & x>3 \end{array}\right.

Explanation:

at x = -3

\begin{aligned} &\lim _{x \rightarrow-3^{+}} f(x)=\lim _{x \rightarrow-3}-2 x=6 \\ &f(-3)=0+3+3=6 \\ &\lim _{x \rightarrow-3^{-}} f(x)=\lim _{x \rightarrow-3}-x+3 \\ &=6 \end{aligned}

Now at x = 3

\begin{aligned} &\lim _{x \rightarrow 3^{-}} f(x)=\lim _{x \rightarrow 3}-2 x=-6 \\ &\quad \lim _{x \rightarrow 3^{+}} f(x)=\lim _{x \rightarrow 3} 6 x+2=20 \\ \end{aligned}

As

\begin{aligned} &\lim _{x \rightarrow 3^{-}} f(x) \neq \lim _{x \rightarrow 3^{+}} f(x) \end{aligned}

f(x) is not continuous at x = 3.

Posted by

Gurleen Kaur

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