EIT Mathematics & Engineering Fundamentals 4

Question 1

The partial derivative ∂/∂x of f(x,y) = x²y + sin(xy) is:

Accepted Answer

2xy + y·cos(xy)

Answer

Treating y as constant: ∂/∂x(x²y) = 2xy and ∂/∂x(sin(xy)) = y·cos(xy) by the chain rule.

Question 2

For the Poisson distribution with mean λ, the variance is:

Accepted Answer

λ

Answer

A unique property of the Poisson distribution is that both its mean and variance equal the parameter λ.

Question 3

The rank of a matrix is defined as the:

Accepted Answer

Number of linearly independent rows (or columns)

Answer

Rank equals the maximum number of linearly independent row vectors (or equivalently column vectors) in the matrix.

Question 4

What does a Bode plot display?

Accepted Answer

Magnitude and phase of a transfer function vs. log frequency

Answer

A Bode plot consists of two graphs: magnitude (in dB) and phase (in degrees) plotted against logarithmic frequency.

Question 5

The inverse Laplace transform of 1/(s² + ω²) is:

Accepted Answer

sin(ωt)/ω

Answer

From standard Laplace transform tables, L{sin(ωt)} = ω/(s²+ω²), so L⁻¹{1/(s²+ω²)} = sin(ωt)/ω.

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