Understanding Maclaurin Series

What is the general form of a Maclaurin series?

• A series that only includes even powers of x

• A series expansion of a function about the point x = 0

• A series expansion of a function about a point a ≠ 0

• A polynomial approximation of a function at infinity

What is the factorial term in the denominator of the nth term in a Maclaurin series?

• (n-1)!

• (n+1)!

• n!

• 2n!

What is the first derivative of sine(x)?

• -sine(x)

• -cosine(x)

• cosine(x)

• sine(x)

What is the pattern of the derivatives for sine(x) in its Maclaurin series?

• They repeat every four terms

• They do not repeat

• They repeat every two terms

• They repeat every three terms

In the Maclaurin series for sine(x), which terms are included?

• Only even powers of x

• No powers of x

• Only odd powers of x

• All powers of x

What is the pattern of signs in the Maclaurin series for sine(x)?

• All negative

• No pattern

• Alternating positive and negative

• All positive

Why does the function x^(1/3) not have a Maclaurin series?

• It is not differentiable at x = 0

• Its derivatives are undefined at x = 0

• It is not continuous at x = 0

• It has a discontinuity at x = 1

What is the value of the first derivative of ln(1 + x) at x = 0?

• 0

• Undefined

• 1

• -1

What is the second derivative of ln(1 + x)?

• -1/(1 + x)

• 1/(1 + x)

• -1/(1 + x)^2

• 1/(1 + x)^2

What is the third derivative of ln(1 + x) at x = 0?

• 2

• -2

• 0

• Undefined