Question

5. Find the value of Lem [fan +160 (1)-- 5. Find the value of Lim an Icos | n->

JEE/Engineering Exams

Maths

Solution

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( lim _{n rightarrow infty} frac{2}{pi}(n+1) cos ^{-1}left(frac{1}{n}right)-n ) ( lim _{n rightarrow infty} nleft[frac{2}{pi}left(1+frac{1}{n}right) cos ^{-1}(1 / n)-1right]=lim _{n rightarrow infty} frac{frac{2}{pi} cos ^{-1}left(frac{1}{n}right)-1}{1 / n} ) ( =lim _{n rightarrow infty} frac{frac{2}{pi} frac{x}{sqrt{1-(1 / n)^{2}}}}{-x_{n}^{2}} leq frac{-2}{pi} times frac{1}{sqrt{5-0}}=frac{-2}{pi} )