Math  /  Calculus

QuestionStandard 16: Problem 4 (1 point) a. Find the Laplace transform F(s)=L{f(t)}F(s)=\mathcal{L}\{f(t)\} of the function f(t)=2e9t+3t+6e10tf(t)=2 e^{-9 t}+3 t+6 e^{10 t}, defined on the interval t0t \geq 0. F(s)=L{2e9t+3t+6e10t}=F(s)=\mathcal{L}\left\{2 e^{-9 t}+3 t+6 e^{10 t}\right\}= \square help (formulas) b. For what values of ss does the Laplace transform exist? \square help (inequalities)
Note: You can earn partial credit on this problem.

Studdy Solution
a. F(s)=2s+9+3s2+6s10F(s) = \frac{2}{s + 9} + \frac{3}{s^2} + \frac{6}{s - 10} b. s>10s > 10

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