Raghid E.

Engineering Technology Graduate Tutor

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Pre-Calculus

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Question:

Find the second order derivative of sin(x^2)

Raghid E.

Answer:

First order derivative = 2xcos(x^2) Second order derivative = -4xsin(x^2)

Calculus

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Question:

Find the Laplace transform of ((t^2) + (e^2)(sin2t))

Raghid E.

Answer:

Use the general table to find t^2 Solution: n!/s^(n+1) Where n is t^n =2!/s^(2+1) =2/s^3 Use S-Shifting (First translation theorem to find (e^2)(sin2t)) Side note: We know to use s shifting due to observing that there is an exponential function (e^2) being multiplied by another function (sin2t) We can use the general formulation of S-Shifting to solve this. First step: We need f(s-a) = F(s) and a is found in e^a and in this case, it is 2 Second Step: Find the general formulation of the Laplace of Sin2t which is k/s^2 + k^2 where k is Sinkt in the formula The Laplace of sin2t is 2/s^2 + 2^2 = 2/(s)^2+4 a = 2 F(s-2) = 2/(s)^2 +4 Now substitute F(s) = 2/(s+2)^2 + 4

Civil Engineering

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Question:

What is beam design governed by?

Raghid E.

Answer:

1) Moment, where the resistance must be greater than the failure 2) Shear 3) Deflection, where the actual deflection must be greater than the limit

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