Generating...                               quiz05_n10

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

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

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

    $\displaystyle e^ {- {{t}\over{3}} }$ $\displaystyle e^ {- 3\,t }$ $\displaystyle 3\,e^ {- 3\,t }$ $\displaystyle {{e^ {- {{t}\over{3}} }}\over{3}}$

  3. Find the Laplace transform for $\displaystyle f\left(t\right)=\left(e^{t}-2\right)\,e^{t}$

    $\displaystyle {{1}\over{s^2-3\,s+2}}$ $\displaystyle {{3\,s-10}\over{s^2-6\,s+8}}$ $\displaystyle -{{s-3}\over{s^2-3\,s+2}}$ $\displaystyle {{3\,s-5}\over{s^2-3\,s+2}}$ $\displaystyle -{{s-6}\over{s^2-6\,s+8}}$

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

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

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

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


Department of Mathematics
Last modified: 2025-10-31