Mathematics-III Exam Prep
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Mathematics-III Exam Prep
Sample questions with model answers
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Find the Laplace transform of $f(t) = 3t^3 – 2e^{2t} + 4 \sin t$.
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$L\{f(t)\} = \frac{6}{s^4} - \frac{2}{s-2} + \frac{4}{s^2 + 1}$
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Find the Laplace transform of $f''(t)$ if $L\{f(t)\} = F(s)$, $f(0) = 2$, $f'(0) = 3$.
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$s^2F(s) - 2s - 3$
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Find $L \{\int_0^t (u^2 + 3u) \ du\}$.
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$\frac{2}{s^3} + \frac{3}{s^2}$
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Find $L\{3\delta(t - 2) + 5\delta(t − 4)\}$.
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$3e^{-2s} + 5e^{-4s}$
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