Generating...                               quiz06_n10

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

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

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

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

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

    $\displaystyle {{2\,s}\over{s^4-8\,s^2+16}}-{{1}\over{s^3-4\,s}}$ $\displaystyle {{s}\over{s^3-2\,s^2-3\,s}}-{{1}\over{s^3-2\,s^2-3\,s}}$ $\displaystyle {{s}\over{s^3-2\,s^2+5\,s}}-{{1}\over{s^3-2\,s^2+5\,s}}$ $\displaystyle {{2\,s}\over{s^4+8\,s^2+16}}-{{1}\over{s^3+4\,s}}$

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

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

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

    $\displaystyle {{\sin t}\over{2}}-{{t\,\cos t}\over{2}}$ $\displaystyle \sin t$ $\displaystyle \cos t$ $\displaystyle {{t\,\sin t}\over{2}}$


Department of Mathematics
Last modified: 2025-10-30