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  • Explain solution RD Sharma class 12 chapter Continuity exercise 8.2 question 9 maths

Explain solution RD Sharma class 12 chapter Continuity exercise 8.2 question 9 maths

Answers (1)

Answer:

 Everywhere continuous

Given:

f(x)=\left\{\begin{array}{cc} 2 x-1 & x<2 \\ \frac{3 x}{2} & x \geq 2 \end{array}\right.

Hint:

Polynomial & identity functions are everywhere continuous. 

Explanation:

As polynomial & identity function are everywhere continuous.

So, we only have to check at end point i.e. x = 2

f(2)=\frac{3 \times 2}{2}=3

\begin{aligned} &\text { L.H.L } =\lim _{x \rightarrow 2^{-}} f(x)=\lim _{h \rightarrow 0}(2-h)=\lim _{h \rightarrow 0} 2(2-h)-1=3 \\ &\text { R.H.L }=\lim _{x \rightarrow 2^{+}} f(x)=\lim _{h \rightarrow 0}(2+h)=\lim _{h \rightarrow 0} \frac{3(2+h)}{2}=3 \\ &\text { L.H.L }=\text { R.H.L }=f(2)=3 \end{aligned}

f(x) is continuous at x = 2 and everywhere

Posted by

Gurleen Kaur

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