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Quiz 4

Mathematics Department
Tennessee Technological University


Date: November 18, 2017


  1. Sketch the graph of $ \displaystyle y=e^{x}+e^ {- x }$

    \includegraphics{thisquiz_pick_plot0.ps}

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  2. Solve the equation $ \displaystyle \ln x=\ln \left(x+2\right)-1$

    [ x = 1 ]

    $ \displaystyle \left[ x={{2}\over{e-1}} \right] $

    $ \displaystyle \left[ x=-{{2\,e}\over{e-1}} \right] $

    [ x = 2 ]

  3. Sketch the graph of $ \displaystyle y={{1}\over{3^{\left\vert x\right\vert }}}$

    \includegraphics{thisquiz_pick_plot4.ps}

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    \includegraphics{thisquiz_pick_plot6.ps}

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  4. Solve the equation $ \displaystyle 5^{x-4}=25$

    [ x = 29 ]

    [ x = 6 ]

    [ x = −2 ]

    [ x = 15625 ]

  5. Solve the equation $ \displaystyle x^2\,e^{x}-5\,x\,e^{x}=0$

    $ \displaystyle \left[ x=-\sqrt{5} , x=\sqrt{5} \right] $

    [ x = 0 ,  x = 5 ]

    $ \displaystyle \left[ x=e , x=e^5 \right] $

    $ \displaystyle \left[ x=0 , x=e^5 \right] $

  6. Solve the equation $ \displaystyle
27
= ( {{1}\over{9}})
3^{2\,x}$

    $ \displaystyle \left[ x={{5}\over{2}} \right] $

    $ \displaystyle \left[ x={{13}\over{9}} \right] $

    [ x = −5 ]

    $ \displaystyle \left[ x={{13}\over{3}} \right] $

  7. Solve the equation $ \displaystyle 2^{x}=4^{1-x}$

    $ \displaystyle \left[ x={{1}\over{2}} \right] $

    $ \displaystyle \left[ x={{\ln 4}\over{\ln 4+\ln 2}} \right] $

    $ \displaystyle \left[ x={{1}\over{\ln 4+\ln 2}} \right] $

    [ x = 1 ]





Department of Mathematics
Last modified: 2017-11-18