Question

Find the following limit analytically. Check my work? o:

Answer 1

\[\lim_{x \rightarrow 0}\frac{\sin(3x)(1-\cos(2x))}{x^2}\]
\[\lim_{x \rightarrow 0}\frac{\sin(3x)}{x} \times\frac{(1-\cos(2x))}{x}\]
\[\lim_{x \rightarrow 0}\frac{3 \cdot \sin(3x)}{3\cdot x}\times \frac{2\cdot (1-\cos(2x))}{2\cdot x}\]
\[\lim_{x \rightarrow 0}\frac{3 \cdot \sin(3x)}{3x} \times\frac{2\cdot (1-\cos(2x))}{2 x}\]
\[\lim_{x \rightarrow 0}\frac{3 \cdot \sin(3x)}{3x} \times\frac{2\cdot (1-\cos(2x))}{2 x}\]
\[\lim_{x \rightarrow 0}3\times 0\]
\[\lim_{x \rightarrow 0}0\]

which is going to be 0? o:

Answer 2

@agent0smith

Answer 3

Wow, nice job.

Answer 4

Ty ty

Harder questions coming right up ;o