Chapter 2.3, Problem 36E

To determine

(a)

To evaluate:

The value of limit of the following function:

$\underset{x\to 0}{\lim }\left[\cos \left(\frac{2x}{1-2x}\right)\right]$.

To determine

(b)

To evaluate:

The value of limit of the following function:

$\underset{x\to \frac{\pi }{2}}{\lim }\left(\frac{\cos x}{x}\right)$.

To determine

(c)

To evaluate:

The value of limit of the following function:

$\underset{x\to 1}{\lim }\left[x^3\cos \left(1-x\right)\right]$.

To determine

(d)

To evaluate:

The value of limit of the following function:

$\underset{x\to 0}{\lim }\left[\frac{1-x^2}{1-\cos \left(x^2\right)}\right]$.