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  • Need solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 4 subquestion (viii)

Need solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 4 subquestion (viii)

Answers (1)

Answer:

 k = 6

Hint:

 Put LHL = RHL =

f(\frac{\pi }{2})

Given:

 f(x)= \begin{cases}\frac{k \cos x}{\pi-2 x} & x<\pi / 2 \\ 3 & x=\pi / 2 \\ \frac{3 \tan ^{2} x}{2 x-\pi} & x \geq 10\end{cases}

Explanation:

At\: \: x = \frac{\pi }{2}

\begin{aligned} &\text { L.H.L }=f(x) \text { at } x=\frac{\pi}{2} \text { is } \\ &=\lim _{x \rightarrow \frac{\pi}{2}} f(x) \\ &=\lim _{h \rightarrow 0}\left(h-\frac{\pi}{2}\right) \end{aligned}

=\lim _{h \rightarrow 0} \frac{k \cos \left(h-\frac{\pi}{2}\right)}{\pi-2\left(h-\frac{\pi}{2}\right)}=\frac{k}{2}

\begin{aligned} &\text { Again } \mathrm{f}\left(\frac{\pi}{2}\right)=3 \\ &\text { L.H.L } =f\left(\frac{\pi}{3}\right) \\ &\therefore \frac{k}{2}=3 \\ &k=6 \end{aligned}

Posted by

Gurleen Kaur

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