JEE MATHEMATICS MCQ: LIMITS

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Application +4 | -1

f: R \rightarrow R

is given by

f(x)=x+1

then the value of

_{n \to \infty }^{\lim }\frac{1}{n}\left[ {f\left( 0 \right) + f\left( {\frac{5}{n}} \right) + f\left( {\frac{{10}}{n}} \right) + .... + f\left( {\frac{{5\left( {n - 1} \right)}}{n}} \right)} \right]

View answer and explanation

Correct option: D

\frac{7}{2}

Option D (

\frac{7}{2}

) is correct because it is the limit of the Riemann sum, which can be evaluated as a definite integral.

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\lim\limits_{n \to \infty } {\left( {1 + \sin \frac{a}{n}} \right)^n}