If f : R → R is given by f ( x ) = x + 1 , then the value of lim n → ∞ 1 n f 0 + f 5 n + f 10 n + … . . + f 5 ( n - 1 ) n is:

Question

If f : R &#8594; R is given by f ( x ) = x + 1 , then the value of lim n &#8594; &#8734; 1 n f 0 + f 5 n + f 10 n + &#8230; . . + f 5 ( n - 1 ) n is:

Aicharya · Accepted Answer

Let I = lim n &#8594; &#8734; 1 n f 0 + f 5 n + f 10 n + &#8230; . . + f 5 ( n - 1 ) n &#8658; I = &#8721; r = 0 n - 1 f 5 r n 1 n &#8658; I = &#8747; 0 1 f 5 x d x &#8658; I = &#8747; 0 1 5 x + 1 d x &#8658; I = 5 x 2 2 + x 0 1 &#8658; I = 5 2 + 1 = 7 2

If f : R → R is given by f ( x ) = x + 1 , then the value of lim n → ∞ 1 n f 0 + f 5 n + f…

Solution

If f : R &#8594; R is given by f ( x ) = x + 1 , then the value of lim n &#8594; &#8734; 1 n f 0 + f 5 n + f…

Solution

If f : R → R is given by f ( x ) = x + 1 , then the value of lim n → ∞ 1 n f 0 + f 5 n + f…