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


  • Variant 3

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

  • Variant 4

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

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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