Polytechnic Mathematics 3

Question 1

What is the Pythagorean theorem for a right triangle with legs a, b and hypotenuse c?

Accepted Answer

a² + b² = c²

Answer

The Pythagorean theorem states that the sum of the squares of the two legs equals the square of the hypotenuse.

Question 2

What is the value of i² where i is the imaginary unit?

Accepted Answer

-1

Answer

By definition, i = √(-1), so i² = -1.

Question 3

Which conic section is defined by the equation x² + y² = r²?

Accepted Answer

Circle

Answer

The equation x² + y² = r² represents a circle of radius r centered at the origin.

Question 4

What is the Taylor series expansion of eˣ centered at x = 0?

Accepted Answer

1 + x + x²/2! + x³/3! + ...

Answer

The Maclaurin series for eˣ is the sum of xⁿ/n! for n from 0 to infinity.

Question 5

What is the formula for the area of a circle?

Accepted Answer

πr²

Answer

The area of a circle is πr², where r is the radius.

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