Find the first four nonzero terms of the Taylor series for the functions in Exercises 1–10.
6. (1 - x/3)^4

Finding Taylor Series at x = 0 (Maclaurin Series)

Find the Maclaurin series for the functions in Exercises 11–24.

5 cos πx

Finding Taylor and Maclaurin Series

In Exercises 25–34, find the Taylor series generated by f at x = a.

f(x) = x³ − 2x + 4,a = 2

Finding Taylor and Maclaurin Series

In Exercises 25–34, find the Taylor series generated by f at x = a.

f(x) = cos(2x + π/2),a = π/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))

Maclaurin Series

Find Taylor series at x = 0 for the functions in Exercises 63–70.

cos (x³/√5)

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