Calculus and Series Quiz

• 1/a*tan(ax) + c

• ln|x| + c

What is the formula for the sum of an arithmetic series Sn?

• Sn = 1/2*n[2a + (n-1)d]

• Sn = n(n+1)/2

• Sn = n(n+1)(2n+1)/6

What is the formula for the sum of a geometric series Sn?

• Sn = n(n+1)/2

• Sn = n(n+1)(2n+1)/6

• Sn = 1/2*n[2a + (n-1)d]

What is the binomial coefficient equal to?

• n!/(r!(n-r)!)

• n!/((n-r)!)

• r!/((n-r)!)

• n!(n-r)!

What is the Maclaurin expansion of f(x)?

• f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

• f(x) = f(0) + f'(0)x + f''(0)x^2/3! + f'''(0)x^3/4! + ...

• f(x) = f(0) + f'(0)x/2! + f''(0)x^2/3! + f'''(0)x^3/4! + ...

• f(x) = f'(0) + f''(0)x/2! + f'''(0)x^2/3! + f''''(0)x^3/4! + ...

What is the result of raising a complex number in polar form \([r(\cos \theta + i\sin \theta)]\) to the power of \(n\) according to De Moivre's theorem?

• A) \(r^n(\cos n\theta + i\sin n\theta)\)

• B) \(r^n(\cos \theta + i\sin \theta)^n\)

• C) \(r(\cos n\theta + i\sin \theta)\)

• D) \(r(\cos \theta + i\sin n\theta)\)

What is the simplified form of the function f(x) = x^-1 ln x, for x > 0 after differentiating with respect to x?

• -x^-2 ln x + x^-1

• x^-2 ln x + x^-1

• -x^-2 ln x - x^-1

• x^-2 ln x - x^-1

What is the derivative of y = cos^-1 4x with respect to x?

• -4/sqrt(1 - 16x^2)

• 4/sqrt(1 - 16x^2)

• -1/(4sqrt(1 - 16x^2))

• 1/(4sqrt(1 - 16x^2)

Is the expression (2 + 3i)/(2 - 3i) - (2 - 3i)/(2 + 3i) real or imaginary?

• Real

• Imaginary

• Complex

• Cannot be determined