Question

Trig Limit Help!

1) lim sin 2 z/z cos 3 z
Z-0

2) lim tan 3x/tan 5x
X-0

3) lim sin^2 theta/theta
Theta-0

4) lim tan 2x/3x
X-0

Answer 1

@tkhunny do you have quick short cuts for these? I think 1= 2 but not sure

Answer 2

No shortcuts. There are a few things you can do.

1) Find a version of sin(W)/W which, when approaching zero is 1. Also, W/sin(W).
2) Is the same true of tan(W)/W? It would be helpful if it were so.

Answer 3

\[\lim_{z \rightarrow 0}\frac{ \sin 2z }{ z \cos 3z }=2\lim_{z \rightarrow 0}\frac{ \sin 2z }{ 2z }*\lim_{z \rightarrow 0}\frac{ 1 }{ \cos 3z }=?\]

Answer 4

\[\lim_{\theta \rightarrow 0}\frac{ \sin ^2\theta }{ \theta }=\lim_{\theta \rightarrow 0}\frac{ \sin ^2\theta }{ \theta^2 } \times \theta \]
\[=\lim_{\theta \rightarrow 0}\left( \frac{ \sin \theta }{ \theta } \right)^2*\lim_{\theta \rightarrow 0}\theta =?\]

Answer 5

i hope you can solve other .