Use the Laplace transform to solve each of the following equations: (a) f'(t) + f(t) = 3 where f(0) = 0 (b) 3f'(t) + 2f (t) = t where f(0) = -2 (c) f"(t) +5f' (t) + 6f (t) = 2e¯¹ where f(0) = 0 and f'(0) = 0

Q: ne hundredth derivative of p (x) (x + x³ + x')1º (1 + x² )11 (x³ + + x Justify ya

A: P(x) = (x+x5+x7 )10(1+x2 )11(x3+x5+x7) Here, (x+x5+x7)10  will have x70 as leading degree. (1+x2)11…

Q: Your used Chevy’s gas mileage (in miles per gallon) is given as a function M(s) of speed s in miles…

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Q: Find h' (t) if h(t) = h'(t)= [] 5 1/3 2 3/7

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Q: The derivative F' (t) is graphed in the figure below. Given that F (0) = 12, calculate F(t) for t =…

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Q: Let Q (p) : %3D p+1 (a) Calculate the derivative Q' (p) (b) Calculate the quotient Q (p + 4) – Q (p)…

A: Using derivative formula.

Q: Find h'(t) if h(t) = h' (t)= 6 1/6 6 5/7

A: We have to find firse derivative of function h(t).

Q: The function f(t) gives the speed of a car in miles per hour, t hours into a journey. Give a single…

A: distance = speed x time the derivative of speed wrt time is acceleration. i.e.,…

Q: Suppose F(8) = 5, F(9)= -23, and - 9 f6f (x) d Your Answer: Answer dx= F'(x) = f(x).

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Q: If f(x) = 15 to dt then f'(x) =

A: Note:-Since you asked multiple questions according to our policy we can answer only first question…

Q: Find f. 13 f"(x)=x³+ sinhx, f(0) = 4, ƒ(2)= 5

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