Generating...                               quiz05_n14

  1. Find the inverse transform for $\displaystyle F\left(s\right)={{1}\over{s^2\,\left(s+1\right)}}$

    $\displaystyle \sin t$ $\displaystyle e^ {- t }+t-1$ $\displaystyle 1-\cos t$ $\displaystyle 1-e^ {- t }$

  2. Find the Laplace transform for $\displaystyle f\left(t\right)=\cos \left(3\,t\right)+\sinh t$

    $\displaystyle {{s}\over{s^2+1}}+{{3}\over{s^2-9}}$ $\displaystyle {{3}\over{s^2+9}}+{{s}\over{s^2-1}}$ $\displaystyle {{s}\over{s^2+9}}+{{1}\over{s^2-1}}$ $\displaystyle {{1}\over{s^2+1}}+{{s}\over{s^2-9}}$

  3. Find the inverse transform for $\displaystyle F\left(s\right)={{s}\over{\left(s-3\right)\,\left(s+1\right)\, \left(s+2\right)}}$

    $\displaystyle {{7\,e^{3\,t}}\over{20}}+{{e^ {- t }}\over{4}}-{{3\,e^ {- 2\,t } }\over{5}}$ $\displaystyle {{e^{3\,t}}\over{10}}-{{e^ {- t }}\over{2}}+{{2\,e^ {- 2\,t } }\over{5}}$ $\displaystyle {{3\,e^{3\,t}}\over{20}}+{{e^ {- t }}\over{4}}-{{2\,e^ {- 2\,t } }\over{5}}$ $\displaystyle {{e^{3\,t}}\over{4}}-{{e^ {- t }}\over{4}}$ $\displaystyle {{3\,e^{3\,t}}\over{10}}+{{e^ {- t }}\over{2}}-{{4\,e^ {- 2\,t } }\over{5}}$

  4. Find the inverse transform for $\displaystyle F\left(s\right)={{1}\over{2\,s+1}}$

    $\displaystyle 2\,e^ {- 2\,t }$ $\displaystyle e^ {- 2\,t }$ $\displaystyle e^ {- {{t}\over{2}} }$ $\displaystyle {{e^ {- {{t}\over{2}} }}\over{2}}$

  5. Find the inverse transform for $\displaystyle F\left(s\right)={{1}\over{s^2+4}}$

    $\displaystyle \cos \left(2\,t\right)$ $\displaystyle {{\sin \left(2\,t\right)}\over{2}}$ $\displaystyle {{\cos \left({{t}\over{2}}\right)}\over{4}}$ $\displaystyle {{\sin \left({{t}\over{2}}\right)}\over{2}}$


Department of Mathematics
Last modified: 2026-02-06