jee-main 2021 Q74

jee-main · India · session3_20jul_shift2 Indefinite & Definite Integrals Definite Integral as a Limit of Riemann Sums

If $f : R \rightarrow R$ is given by $f ( x ) = x + 1$, then the value of $\lim _ { n \rightarrow \infty } \frac { 1 } { n } \left[ f ( 0 ) + f \left( \frac { 5 } { n } \right) + f \left( \frac { 10 } { n } \right) + \ldots + f \left( \frac { 5 ( n - 1 ) } { n } \right) \right]$ is:
(1) $\frac { 3 } { 2 }$
(2) $\frac { 5 } { 2 }$
(3) $\frac { 1 } { 2 }$
(4) $\frac { 7 } { 2 }$

If $f : R \rightarrow R$ is given by $f ( x ) = x + 1$, then the value of\\
$\lim _ { n \rightarrow \infty } \frac { 1 } { n } \left[ f ( 0 ) + f \left( \frac { 5 } { n } \right) + f \left( \frac { 10 } { n } \right) + \ldots + f \left( \frac { 5 ( n - 1 ) } { n } \right) \right]$ is:\\
(1) $\frac { 3 } { 2 }$\\
(2) $\frac { 5 } { 2 }$\\
(3) $\frac { 1 } { 2 }$\\
(4) $\frac { 7 } { 2 }$

Paper Questions

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