Maclaurin Series
Find Taylor series at x = 0 for the functions in Exercises 63–70.
cos (x³/√5)

Find the first four nonzero terms of the Taylor series for the functions in Exercises 1–10.

6. (1 - x/3)^4

Use series to evaluate the limits in Exercises 29–40.

29. lim (x → 0) (e^x - (1 + x)) / x²

Use series to evaluate the limits in Exercises 29–40.

37. lim (x → 0) ln(1 + x²) / (1 - cos(x))

Finding Taylor Series

Use substitution (as in Formula (7)) to find the Taylor series at x = 0 of the functions in Exercises 1–12.

e⁻ˣ/²

Use power series operations to find the Taylor series at x = 0 for the functions in Exercises 13–30.

sin x – x + (x³ / 3!)

30. b. By differentiating the series in part (a) term by term, show that

Σ(from n=1 to ∞) n / (n + 1)! = 1.