Exploring McLaurin Series

• 1

• infinity

• 5

• 2

Calculate the first three derivatives of f(x) = sin(x) at x = 0.

• f'(0) = 0, f''(0) = 1, f'''(0) = 1

• f'(0) = -1, f''(0) = 0, f'''(0) = 0

• f'(0) = 1, f''(0) = 0, f'''(0) = -1

• f'(0) = 1, f''(0) = -1, f'''(0) = 0

Which of the following functions can be represented by a McLaurin series?

• Quadratic functions

• Logarithmic functions

• Exponential functions, sine functions, and cosine functions.

• Absolute value functions

If the McLaurin series for f(x) converges for all x, what can be said about the function f(x)?

• f(x) is a polynomial function.

• f(x) is not differentiable at any point.

• f(x) has a finite number of singularities.

• f(x) is an entire function.

Using the McLaurin series, what is the approximation of f(x) = ln(1+x) at x = 0?

• 0.5

• -1

• 1

• 0