Fundamentals of Engineering Engineering Mathematics 2

Question 1

What does the Fourier series represent for a periodic function?

Accepted Answer

A sum of sinusoidal components at integer multiples of the fundamental frequency

Answer

The Fourier series decomposes a periodic function into sinusoidal components at integer multiples of the fundamental frequency.

Question 2

In probability, if events A and B are mutually exclusive, then P(A ∪ B) equals:

Accepted Answer

P(A) + P(B)

Answer

For mutually exclusive events, P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B).

Question 3

What is the general solution to the ordinary differential equation dy/dx + 2y = 0?

Accepted Answer

y = Ce^(-2x)

Answer

This first-order linear ODE has solution y = Ce^(-2x) obtained by separation of variables.

Question 4

The Taylor series expansion of sin(x) about x = 0 begins with which terms?

Accepted Answer

x - x³/6 + x⁵/120 - ...

Answer

The Maclaurin series of sin(x) is x - x³/3! + x⁵/5! - ..., which matches x - x³/6 + x⁵/120.

Question 5

Which of the following is the correct formula for the determinant of a 2×2 matrix [a b; c d]?

Accepted Answer

ad - bc

Answer

The determinant of a 2×2 matrix is calculated as ad - bc.

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