Generating...                               quiz06_n21

  1. Find the Laplace transform for $\displaystyle f\left(t\right)=\int_{0}^{t}{e^{u}\,\sinh \left(2\,u\right)\;du}$

    $\displaystyle {{2\,s}\over{s^4-8\,s^2+16}}-{{1}\over{s^3-4\,s}}$ $\displaystyle {{4}\over{s^4-8\,s^2+16}}$ $\displaystyle {{2}\over{s^3-2\,s^2-3\,s}}$ $\displaystyle {{s}\over{s^3-2\,s^2-3\,s}}-{{1}\over{s^3-2\,s^2-3\,s}}$

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

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

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

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

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

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

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

    $\displaystyle {{s-2}\over{s^2-4\,s+8}}$ $\displaystyle {{s-2}\over{s^2-4\,s+5}}$ $\displaystyle {{1}\over{s^2-4\,s+5}}$ $\displaystyle {{2}\over{s^2-4\,s+8}}$


Department of Mathematics
Last modified: 2025-09-14