EIT Mathematics & Engineering Fundamentals 5

Question 1

Which interpolation method fits a polynomial of degree n-1 exactly through n data points?

Accepted Answer

Lagrange interpolation

Answer

Lagrange interpolation constructs a unique polynomial of degree at most n-1 that passes exactly through all n given data points.

Question 2

If A and B are mutually exclusive events, then P(A ∪ B) equals:

Accepted Answer

P(A) + P(B)

Answer

Mutually exclusive events cannot occur simultaneously, so P(A ∩ B) = 0 and the addition rule simplifies to P(A) + P(B).

Question 3

The determinant of a 2×2 matrix [[a, b],[c, d]] is:

Accepted Answer

ad - bc

Answer

The 2×2 determinant is computed as the product of the main diagonal minus the product of the anti-diagonal: ad - bc.

Question 4

The solution to the first-order linear ODE dy/dt + 2y = 0 with y(0) = 5 is:

Accepted Answer

y = 5e^(-2t)

Answer

Separating variables gives dy/y = -2dt, integrating yields ln|y| = -2t + C, and applying y(0) = 5 gives y = 5e^(-2t).

Question 5

The trapezoidal rule approximates a definite integral by treating the integrand as:

Accepted Answer

A straight line between adjacent points

Answer

The trapezoidal rule connects adjacent function values with straight lines, computing the area of resulting trapezoids.

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