Generating...                               quiz05_n3

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

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

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

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

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

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

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

    $\displaystyle {{3\,s+2}\over{s^3}}$ $\displaystyle -{{s-6}\over{s^2-6\,s+8}}$ $\displaystyle {{3\,s-10}\over{s^2-6\,s+8}}$ $\displaystyle {{4\,s-14}\over{s^2-6\,s+8}}$ $\displaystyle {{2\,s+2}\over{s^3}}$

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

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


Department of Mathematics
Last modified: 2026-09-10