Shape of a function (without convexity)

Task number: 3048

Investigate the shape of the following functions including their asymptotes and limits at boundary points of the domain of definition (you need not investigate convexity). Sketch their graphs.

  • Variant 1

    \(\displaystyle f(x)=\sin(\sin(x))\)

  • Variant 2

    \(\displaystyle f(x)=\sin(\pi \sin x)\)

  • Variant 3

    \(\displaystyle f(x)=\frac{x}{\sin x}\) (in this variant you will probably not determine the extrema precisely, but try to at least estimate their positions)

  • Variant 4

    \(\displaystyle f(x)=2x^2(x - \sqrt{x^2 - 1})\)

  • Variant 5

    \(\displaystyle f(x)=\sin \left( \frac{1}{|x| + 2/(3 \pi)}\right)\)

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