Question

How do you figure out the limit of sin^2(5x)/(5x^2)

Answer 1

x approaches?

Answer 2

as x approaches 0, sorry, forgot that!

Answer 3

\[\\ \lim_{u \rightarrow 0} \frac{\sin(u)}{u}=1 \\\]

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\[\lim_{x \rightarrow 0} \frac{\sin^2(5x)}{5x^2} \\ \lim_{x \rightarrow 0} \frac{\sin(5x) \cdot \sin(5x)}{5x^2} \\ \lim_{x \rightarrow 0} \frac{\sin(5x)}{5x} \cdot \frac{\sin(5x)}{5x} \cdot 5\]

Answer 4

could you continue from here?

Answer 5

yes, thank you!