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Class-11-science»Maths

Please solve question no 13 and 14

Dear student,

Q n o 13, F o r t h e l i m i t t o e x i s t w e s h a l l h a v e \underset{x \to 1}{l i m} (f (x) - 2) = 0 i . e \underset{x \to 1}{l i m} f (x) = 2 Q n o 14 \sqrt{(1 - \cos (\frac{1}{n})) \sqrt{(1 - \cos (\frac{1}{n})) \sqrt{(1 - \cos (\frac{1}{n})) \sqrt{(1 - \cos (\frac{1}{n})} . . . \infty}}} = {((1 - \cos (\frac{1}{n})))}^{\frac{1}{2} + \frac{1}{4} + . . . \infty} = {((1 - \cos (\frac{1}{n})))}^{\frac{\frac{1}{2}}{1 - \frac{1}{2}}} = 1 - \cos (\frac{1}{n}) = 2 \sin^{2} (\frac{1}{2 n}) H e n c e l i m i t e q u a l s \underset{\frac{1}{2 n} \to 0}{l i m} \frac{2 \sin^{2} (\frac{1}{2 n})}{{(\frac{1}{2 n})}^{2}} \times \underset{n \to \infty}{l i m} {(\frac{1}{2 n})}^{2} \times n^{2} = 2 \times \frac{1}{4} = \frac{1}{2}

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