Removable discontinuities
Task number: 2987
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
\( f(x)=x^3\sin^2\frac1x \)