Questions from Calculus

Q: Find the Taylor series at x = 0 of the given function

Find the Taylor series at x = 0 of the given function by computing three or four derivatives and using the definition of the Taylor series. ln(1 - 3x)

Q: State the remainder formula for the nth Taylor polynomial of f (

State the remainder formula for the nth Taylor polynomial of f (x) at x = a.

Q: Explain how the Newton–Raphson algorithm is used to approximate a

Explain how the Newton–Raphson algorithm is used to approximate a zero of a function.

Q: Determine the nth Taylor polynomial of f (x) = 1

Determine the nth Taylor polynomial of f (x) = 1/x at x = 1.

Q: What is the nth partial sum of an infinite series?

What is the nth partial sum of an infinite series?

Q: What is a convergent infinite series? Divergent?

What is a convergent infinite series? Divergent?

Q: What is meant by the sum of a convergent infinite series?

What is meant by the sum of a convergent infinite series?

Q: What is a geometric series and when does it converge?

What is a geometric series and when does it converge?

Q: What is the sum of a convergent geometric series?

What is the sum of a convergent geometric series?

Q: Define the Taylor series of f (x) at x =

Define the Taylor series of f (x) at x = 0.