Is the function $f$ defined by $f\left(x\right)=\cos \left|x\right|$ a continuous function $?$

Prove that the function is continuous:

$\frac{2x^3-7x^2+3}{\left(x-1\right)\left(x+3\right)}$

Prove that the function is continuous:

$\left|\sec x +\tan x\right|$

Examine the function for continuity.

$\cos \left(x^2\right)$

Examine the function for continuity.

$\sin \left(3x^2-5\right)$

Examine the function for continuity.

$ta{n}^{-1} \left(2x^2+3\right)$