<p><strong> Let <math><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mi>x</mi></mrow><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mrow><mtable><mtr columnalign="center"><mtd columnalign="center"><mfrac><mrow><mi>k</mi><mo> </mo><mi>c</mi><mi>o</mi><mi>s</mi><mi>x</mi></mrow><mrow><mi>π</mi><mo>−</mo><mn>2</mn><mi>x</mi></mrow></mfrac><mo> </mo></mtd><mtd columnalign="center">when <mi>x</mi><mo>≠</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo></mtd></mtr><mtr columnalign="center"><mtd columnalign="center"><mn>3</mn></mtd><mtd columnalign="center">when <mi>x</mi><mo>=</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mtd></mtr></mtable></mrow></mrow></mrow></math> , and if <math><mrow><mi>l</mi><mi>i</mi><msub><mrow><mi>m</mi></mrow><mrow><mi>x</mi><mo>→</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msub><mi>f</mi><mrow><mo>(</mo><mrow><mi>x</mi></mrow><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mrow><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math> , find the value of <math><mrow><mi>k</mi></mrow></math></strong></p>

This is a Short Answer Type Questions as classified in NCERT ExemplarSol:Given f(x)={kcosxπ−2x when x≠π2,3when x=π2 LHL f(x)=limx→π2−kcosxπ−2x=limh→0kcos(π2−h)π−2(π2−h) =limh→0ksinhπ−π+2h=limh→0ksinh2h=k2.1=k2 [?limx→0sinxx=1] RHL f(x)=limx→π2+kcosxπ−2x=limh→0kcos(π2+h)π−2(π2+h) =limh→0−ksinhπ−π−2h=limh→0−ksinh−2h=k2 [?limx→0sinxx=1]We are given that limx→π2f(x)=3So, k2=3 ⇒k=6

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Maths Class 11th Exemplar Solution Limits and Derivatives Maths NCERT Exemplar Solutions Class 11th Chapter Thirteen

Let $f (x) = {\begin{matrix} \frac{k c o s x}{π - 2 x} & when x \neq \frac{π}{2}, \\ 3 & when x = \frac{π}{2} \end{matrix}$ , and if $l i m_{x \to \frac{π}{2}} f (x) = f (\frac{π}{2})$ , find the value of $k$

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alok kumar singh | Contributor-Level 10

2 months ago

This is a Short Answer Type Questions as classified in NCERT Exemplar

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$\begin{array}{l} G i v e n f (x) = {\begin{matrix} \frac{k c o s x}{π - 2 x} & w h e n x \neq \frac{π}{2}, \\ 3 & w h e n x = \frac{π}{2} \end{matrix} \\ L H L f (x) = \underset{x \to {\frac{π}{2}}^{-}}{l i m} \frac{k c o s x}{π - 2 x} = \underset{h \to 0}{l i m} \frac{k c o s (\frac{π}{2} - h)}{π - 2 (\frac{π}{2} - h)} \\ = \underset{h \to 0}{l i m} \frac{k s i n h}{π - π + 2 h} = \underset{h \to 0}{l i m} \frac{k s i n h}{2 h} = \frac{k}{2} . 1 = \frac{k}{2} [? \underset{x \to 0}{l i m} \frac{s i n x}{x} = 1] \\ R H L f (x) = \underset{x \to {\frac{π}{2}}^{+}}{l i m} \frac{k c o s x}{π - 2 x} = \underset{h \to 0}{l i m} \frac{k c o s (\frac{π}{2} + h)}{π - 2 (\frac{π}{2} + h)} \\ = \underset{h \to 0}{l i m} \frac{- k s i n h}{π - π - 2 h} = \underset{h \to 0}{l i m} \frac{- k s i n h}{- 2 h} = \frac{k}{2} [? \underset{x \to 0}{l i m} \frac{s i n x}{x} = 1] \\ W e a r e g i v e n t h a t \underset{x \to \frac{π}{2}}{l i m} f (x) = 3 \\ S o, \frac{k}{2} = 3 \Rightarrow k = 6 \end{array}$

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Let $f (x) = {\begin{matrix} \frac{k c o s x}{π - 2 x} & when x \neq \frac{π}{2}, \\ 3 & when x = \frac{π}{2} \end{matrix}$ , and if $l i m_{x \to \frac{π}{2}} f (x) = f (\frac{π}{2})$ , find the value of $k$

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Let f(x)={k cosxπ−2x when x≠π2,3when x=π2 , and if limx→π2f(x)=f(π2) , find the value of k

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Let $f (x) = {\begin{matrix} \frac{k c o s x}{π - 2 x} & when x \neq \frac{π}{2}, \\ 3 & when x = \frac{π}{2} \end{matrix}$ , and if $l i m_{x \to \frac{π}{2}} f (x) = f (\frac{π}{2})$ , find the value of $k$