Questions from Calculus

Q: Discuss the three possibilities for the radius of convergence of a Taylor

Discuss the three possibilities for the radius of convergence of a Taylor series.

Q: Define the nth Taylor polynomial of f (x) at x

Define the nth Taylor polynomial of f (x) at x = a.

Q: In what way is the nth Taylor polynomial of f (x

In what way is the nth Taylor polynomial of f (x) at x = a like f (x) at x = a?

Q: Find the nth Taylor polynomial of 2/(2 – x)

Find the nth Taylor polynomial of 2/(2 – x) at x = 0.

Q: Determine the third Taylor polynomial of the given function at x =

Determine the third Taylor polynomial of the given function at x = 0. f (x) = xe3x

Q: If f (x) = 3 + 4x – 5/

If f (x) = 3 + 4x – 5/2! x2 + 7/3! x3, what are f ’’(0) and f ’’’(0)?

Q: Find the third Taylor polynomial of x2 at x = 3.

Find the third Taylor polynomial of x2 at x = 3.

Q: Find the third Taylor polynomial of ex at x = 2.

Find the third Taylor polynomial of ex at x = 2.

Q: Use a second Taylor polynomial at t = 0 to estimate the

Use a second Taylor polynomial at t = 0 to estimate the area under the graph of y = -ln(cos 2t) between t = 0 and t = 1/2.

Q: Use a second Taylor polynomial at x = 0 to estimate the

Use a second Taylor polynomial at x = 0 to estimate the value of tan(.1).