NCEES Mathematics 3

Question 1

What is the magnitude of the vector v = 3i + 4j?

Accepted Answer

5

Answer

|v| = √(3² + 4²) = √(9 + 16) = √25 = 5.

Question 2

The Taylor series expansion of e^x centered at x = 0 begins with:

Accepted Answer

1 + x + x²/2! + x³/3! + ...

Answer

The Maclaurin series for e^x is the sum of xⁿ/n! from n=0 to ∞.

Question 3

Which conic section is described by the equation x²/9 + y²/4 = 1?

Accepted Answer

Ellipse

Answer

The equation x²/a² + y²/b² = 1 (with a ≠ b) defines an ellipse.

Question 4

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

Accepted Answer

3

Answer

A·B = (2)(4) + (-1)(2) + (3)(-1) = 8 - 2 - 3 = 3.

Question 5

What is lim(x→0) [sin(x)/x]?

Accepted Answer

1

Answer

This is a standard limit; lim(x→0) sin(x)/x = 1.

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