Generating...                               quiz06_n7

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

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

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

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

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

    $\displaystyle {{e^{3\,t}\,\sin \left(3\,t\right)}\over{3}}$ $\displaystyle {{e^{6\,t}}\over{6}}-{{1}\over{6}}$ $\displaystyle e^{3\,t}\,\left(\sin \left(3\,t\right)+\cos \left(3\,t\right) \right)$ $\displaystyle e^{6\,t}$

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

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


Department of Mathematics
Last modified: 2025-05-04