Generating...                               quiz06_n3

  1. Find the inverse transform for $\displaystyle F\left(s\right)={{1}\over{s^2-6\,s+8}}$

    $\displaystyle {{e^{6\,t}}\over{6}}-{{1}\over{6}}$ $\displaystyle {{e^{4\,t}}\over{2}}-{{e^{2\,t}}\over{2}}$ $\displaystyle e^{6\,t}$ $\displaystyle 2\,e^{4\,t}-e^{2\,t}$

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

    $\displaystyle {{s}\over{s^2-2\,s-8}}-{{1}\over{s^2-2\,s-8}}$ $\displaystyle {{3}\over{s^2-2\,s-8}}$ $\displaystyle {{6\,s}\over{s^4-18\,s^2+81}}$ $\displaystyle {{2\,s^2}\over{s^4-18\,s^2+81}}-{{1}\over{s^2-9}}$

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

    $\displaystyle {{6}\over{\left(s+2\right)^4}}$ $\displaystyle {{2}\over{\left(s+2\right)^3}}$ $\displaystyle {{6}\over{\left(s-2\right)^4}}$ $\displaystyle {{1}\over{s+2}}$ $\displaystyle {{2}\over{\left(s-2\right)^3}}$

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

    $\displaystyle {{s+3}\over{s^2+6\,s+18}}$ $\displaystyle {{s+3}\over{s^2+6\,s+10}}$ $\displaystyle {{3}\over{s^2+6\,s+18}}$ $\displaystyle {{1}\over{s^2+6\,s+10}}$

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

    $\displaystyle \cos \left(2\,t\right)$ $\displaystyle {{\sin \left(2\,t\right)}\over{2}}$ $\displaystyle {{t\,\sin \left(2\,t\right)}\over{4}}$ $\displaystyle {{\sin \left(2\,t\right)}\over{16}}-{{t\,\cos \left(2\,t\right) }\over{8}}$


Department of Mathematics
Last modified: 2026-07-16