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

A polynomial approximation of the function

Answer

A Taylor expansion about a point

Answer

A complex exponential representation only

Question 2

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

Accepted Answer

P(A) + P(B)

Answer

P(A) × P(B)

Answer

P(A) + P(B) - P(A ∩ B)

Answer

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

y = Ce^(2x)

Answer

y = C·sin(2x)

Answer

y = C + 2x

Question 4

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

Accepted Answer

x - x³/6 + x⁵/120 - ...

Answer

1 - x²/2 + x⁴/24 - ...

Answer

x + x³/6 + x⁵/120 + ...

Answer

1 + x + x²/2 + ...

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

ac - bd

Answer

ab - cd

Answer

ad + bc

Question 6

What is the dot product of vectors A = (2, 3, 1) and B = (1, -1, 4)?

Accepted Answer

3

Answer

6

Answer

-1

Answer

7