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Limits Continuity and Differentiability question

2021 · 20 Jul · Shift 2 · Q30
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  5. /2021 · 20 Jul · Shift 2 · Q30

Limits Continuity and Differentiability question

2021 · 20 Jul · Shift 2 · Q30

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1
If f:R→Rf:R \to Rf:R→R is given by f(x)=x+1f(x) = x + 1f(x)=x+1, then the value of lim⁡n→∞1n[f(0)+f(5n)+f(10n)+......+f(5(n−1)n)]\mathop {\lim }\limits_{n \to \infty } {1 \over n}\left[ {f(0) + f\left( {{5 \over n}} \right) + f\left( {{{10} \over n}} \right) + ...... + f\left( {{{5(n - 1)} \over n}} \right)} \right]n→∞lim​n1​[f(0)+f(n5​)+f(n10​)+......+f(n5(n−1)​)] is :
  1. A
    32{3 \over 2}23​
  2. B
    52{5 \over 2}25​
  3. C
    12{1 \over 2}21​
  4. D
    72{7 \over 2}27​
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