## Removable discontinuities

Determine whether the following functions can be made be continuous by defining a value at $$x=0$$. The functions are defined on $$\mathbb R\setminus\{0\}$$ by the following formulas:

• #### Variant 1

$$f(x)=e^{|x|}$$

• #### Variant 2

$$f(x)=\arctan\frac1{x^2}$$

• #### Variant 3

$$f(x)=\frac{1-\cos x}{x^3}$$

• #### Variant 4

$$f(x)=x^3\sin^2\frac1x$$