The constants and satisfy both of the following equalities: _ n _ i=1 ^ n (m ( 4i n…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The constants

m

and

b

satisfy both of the following equalities:

\lim_{n\to\infty}\sum_{i=1}^{n}\bigl(m\left(\tfrac{4i}{n}\right)+b\bigr)\frac{4}{n}=40

and

\lim_{n\to\infty}\sum_{i=1}^{n}\bigl(m\left(\tfrac{2i}{n}\right)+b\bigr)\frac{2}{n}=12.

Which ordered pair

(m,b)

satisfies these conditions? (a)

(3,3)

(b)

(4,-2)

(c)

(4,2)

(d)

(2,2)