EIT Mathematics and Statistics 2

Question 1

The Laplace transform of f(t) = t·e^(2t) is:

Accepted Answer

1/(s-2)²

Answer

Using the Laplace transform formula L{t·e^(at)} = 1/(s-a)², with a=2, the result is 1/(s-2)².

Question 2

Which numerical method uses the formula x_{n+1} = x_n - f(x_n)/f'(x_n) to find roots?

Accepted Answer

Newton-Raphson method

Answer

The Newton-Raphson method iteratively refines root estimates using the function and its derivative.

Question 3

A dataset has mean μ = 50 and standard deviation σ = 5. What percentage of data falls within one standard deviation of the mean, assuming a normal distribution?

Accepted Answer

68%

Answer

The empirical rule states that approximately 68% of data in a normal distribution falls within ±1σ of the mean.

Question 4

The determinant of the matrix [[3,1],[2,4]] equals:

Accepted Answer

10

Answer

det = (3)(4) - (1)(2) = 12 - 2 = 10.

Question 5

Which of the following is the correct expression for the Taylor series expansion of e^x about x=0?

Accepted Answer

Σ x^n/n! for n=0 to ∞

Answer

The Maclaurin series for e^x is 1 + x + x²/2! + x³/3! + … = Σ x^n/n!.

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EIT Mathematics and Statistics 2