Generating...                               quiz05_n16

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

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

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

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

  3. Find the inverse transform for $\displaystyle F\left(s\right)={{s}\over{16\,s^2+1}}$

    $\displaystyle {{\sin \left({{t}\over{4}}\right)}\over{4}}$ $\displaystyle {{\cos \left({{t}\over{4}}\right)}\over{16}}$ $\displaystyle \cos \left(4\,t\right)$ $\displaystyle {{\sin \left(4\,t\right)}\over{4}}$

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

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

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

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


Department of Mathematics
Last modified: 2026-07-16