Generating...                               quiz06_n4

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

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

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

    $\displaystyle {{s+2}\over{s^2+4\,s+13}}$ $\displaystyle {{s+2}\over{s^2+4\,s+8}}$ $\displaystyle {{3}\over{s^2+4\,s-5}}$ $\displaystyle {{2}\over{s^2+4\,s}}$

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

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

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

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

  5. Find the inverse transform for $\displaystyle F\left(s\right)=-{{s}\over{\left(s^2+9\right)^2}}$

    $\displaystyle {{\cos \left(3\,t\right)}\over{2}}$ $\displaystyle -{{t\,\cos \left(3\,t\right)}\over{2}}$ $\displaystyle -{{t\,\sin \left(3\,t\right)}\over{6}}$ $\displaystyle {{\sin \left(3\,t\right)}\over{6}}$


Department of Mathematics
Last modified: 2026-03-24