Generating...                               quiz05_n28

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

    $\displaystyle {{e^{3\,t}}\over{6}}-{{e^{2\,t}}\over{5}}+{{e^ {- 3\,t }}\over{30}}$ $\displaystyle {{5\,e^{3\,t}}\over{6}}-{{4\,e^{2\,t}}\over{5}}-{{e^ {- 3\,t } }\over{30}}$ $\displaystyle {{e^{3\,t}}\over{3}}-{{2\,e^{2\,t}}\over{5}}+{{e^ {- 3\,t }}\over{ 15}}$ $\displaystyle {{e^{3\,t}}\over{2}}-{{2\,e^{2\,t}}\over{5}}-{{e^ {- 3\,t }}\over{ 10}}$ $\displaystyle {{7\,e^{3\,t}}\over{6}}-e^{2\,t}-{{e^ {- 3\,t }}\over{6}}$

  2. Find the inverse transform for $\displaystyle F\left(s\right)={{1}\over{9\,s^2+1}}$

    $\displaystyle \cos \left(3\,t\right)$ $\displaystyle {{\sin \left(3\,t\right)}\over{3}}$ $\displaystyle {{\cos \left({{t}\over{3}}\right)}\over{9}}$ $\displaystyle {{\sin \left({{t}\over{3}}\right)}\over{3}}$

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

    $\displaystyle {{2\,\sin \left(2\,t\right)}\over{5}}+{{\cos \left(2\,t\right) }\over{5}}-{{e^ {- t }}\over{5}}$ $\displaystyle {{2\,\sin t}\over{5}}-{{\cos t}\over{5}}+{{e^ {- 2\,t }}\over{5}}$ $\displaystyle {{\sin t}\over{5}}+{{2\,\cos t}\over{5}}-{{2\,e^ {- 2\,t }}\over{5 }}$ $\displaystyle {{\sin \left(2\,t\right)}\over{10}}-{{\cos \left(2\,t\right)}\over{ 5}}+{{e^ {- t }}\over{5}}$

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

    $\displaystyle e^ {- 4\,t }$ $\displaystyle e^ {- {{t}\over{4}} }$ $\displaystyle {{e^ {- {{t}\over{4}} }}\over{4}}$ $\displaystyle 4\,e^ {- 4\,t }$

  5. Find the Laplace transform for $\displaystyle f\left(t\right)=\cosh \left(2\,t\right)+\sin t$

    $\displaystyle {{1}\over{s^2+1}}+{{s}\over{s^2-4}}$ $\displaystyle {{s}\over{s^2+1}}+{{2}\over{s^2-4}}$ $\displaystyle {{2}\over{s^2+4}}+{{s}\over{s^2-1}}$ $\displaystyle {{s}\over{s^2+4}}+{{1}\over{s^2-1}}$


Department of Mathematics
Last modified: 2026-10-30