Generating...                               quiz05_n14

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

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

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

    $\displaystyle {{3\,s-10}\over{s^2-6\,s+8}}$ $\displaystyle {{4\,s-14}\over{s^2-6\,s+8}}$ $\displaystyle -{{s-6}\over{s^2-6\,s+8}}$ $\displaystyle {{4\,s-7}\over{s^2-3\,s+2}}$ $\displaystyle {{3\,s-5}\over{s^2-3\,s+2}}$

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

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

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

    $\displaystyle {{e^{3\,t}}\over{2}}-{{e^{t}}\over{2}}$ $\displaystyle {{7\,e^{3\,t}}\over{6}}-{{3\,e^{t}}\over{2}}+{{1}\over{3}}$ $\displaystyle {{e^{3\,t}}\over{3}}-e^{t}+{{2}\over{3}}$ $\displaystyle {{5\,e^{3\,t}}\over{6}}-{{3\,e^{t}}\over{2}}+{{2}\over{3}}$ $\displaystyle {{e^{3\,t}}\over{6}}-{{e^{t}}\over{2}}+{{1}\over{3}}$

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

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


Department of Mathematics
Last modified: 2026-05-20