# Math Help - To Evaluate the following limit...

1. ## To Evaluate the following limit...

I need some help in a problem from Calculus 1 class:

Find the lim sin3t + 4t
tsect

when t approaches 0.

2. Originally Posted by thaliaj_df
Find the lim sin3t + 4t
tsect

when t approaches 0.
To learn how to format using only text, try here. My guess as to your meaning, using LaTeX formatting, is as follows:

. . . . . $\lim_{t \rightarrow 0}\, \frac{\sin(3t)\, +\, 4t}{t \sec(t)}$

A good way to start might be to split the addition into two parts, also converting the reciprocal of the secant into a cosine:

. . . . . $\lim_{t \rightarrow 0}\, \frac{\sin(3t)\, cos(t)}{t}\, +\, 4\cos(t)$

You learned an important trig limit, probably when you were learning trig derivatives:

. . . . . $\lim_{\theta \rightarrow 0}\, \frac{\sin(\theta)}{\theta}\, =\, 1$

With this in mind, restate the limit as:

. . . . . $\lim_{t \rightarrow 0}\, 3\left(\frac{\sin(3t)}{3t}\right) \cos(t)\, +\, \lim_{t \rightarrow 0}\, 4\cos(t)$

The cosine can be simply evaluated, and the sine fraction is the limit they gave you earlier.