Question

1. evaluate each limit.

(a) \\( \lim _ { x \
ightarrow 0 } \frac { \cos ^ { 2 } x } { 1 + \tan x } \\)

Explanation:

Step1: Substitute \(x = 0\) into the function

We know that \(\cos(0)=1\) and \(\tan(0) = 0\).
Substitute \(x = 0\) into \(\frac{\cos^{2}x}{1+\tan x}\), we get \(\frac{\cos^{2}(0)}{1+\tan(0)}\).

Step2: Calculate the value

Since \(\cos(0) = 1\), then \(\cos^{2}(0)=1^{2}=1\), and \(\tan(0) = 0\).
So \(\frac{\cos^{2}(0)}{1+\tan(0)}=\frac{1}{1 + 0}\).

Answer:

\(1\)