AP Calculus ABhardmcq1 pt

limx0sin(3x)sin(5x)=\lim_{x\to 0}\dfrac{\sin(3x)}{\sin(5x)}=

A.53\frac{5}{3}
B.11
C.35\frac{3}{5}
D.00

Explanation

Core Concept

Write sin(3x)sin(5x)=sin(3x)3x5xsin(5x)35\frac{\sin(3x)}{\sin(5x)}=\frac{\sin(3x)}{3x}\cdot\frac{5x}{\sin(5x)}\cdot\frac{3}{5}. Each sine ratio approaches 11, so the limit is 35\frac{3}{5}.

Correct Answer

C35\frac{3}{5}

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