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Shape of a function (with convexity)

Task number: 3049

Investigate the shape of the following functions including their asymptotes, limits at boundary points of the domain of definition, and convexity. Sketch their graphs.

  • Variant 1

    f(x)=x312x+16

  • Variant 2

    \displaystyle f(x)=\arcsin(\cos x)

  • Variant 3

    \displaystyle f(x)=\ln^3(x)

  • Variant 4

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

  • Variant 5

    \displaystyle f(x)=\ln(4{\cdot}3^x + 2)

  • Variant 6

    \displaystyle f(x)=\ln\left(\left|\tan\frac{x}4\right|\right)

  • Variant 7

    \displaystyle f(x)=\arcsin\left(\frac{2x}{x^2 + 1}\right)

  • Variant 8

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

  • Variant 9

    \displaystyle f(x)=\frac{x^3}{(x-2)^2}

  • Variant 10

    \displaystyle f(x)=x-\ln(x+1)

  • Variant 11

    \displaystyle f(x)=x\, e^{-|x-1|}

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