Generating...                               quiz06_n1

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

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

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

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

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

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

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

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

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

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


Department of Mathematics
Last modified: 2026-10-28