AP Calculus ABmediummcq1 pt

What is the value of limni=1n3n(1+3in)\lim_{n\to\infty} \sum_{i=1}^{n} \frac{3}{n}\left(1+\frac{3i}{n}\right)?

A.152\frac{15}{2}
B.92\frac{9}{2}
C.33
D.66

Explanation

Core Concept

The limit is 03(1+x)dx=[x+x2/2]03=3+9/2=15/2\int_0^3(1+x)\,dx=[x+x^2/2]_0^3=3+9/2=15/2.

Correct Answer

A152\frac{15}{2}

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