Find the Fourth Term of the Taylor Series for the Function

question 13

Multiple Choice

Find the fourth term of the Taylor series for the function $f(x) =\cos x$ about $x=\pi / 3$ .

• A) \(\frac{\left(x-\frac{\pi}{3}\right)^{3}}{12}\)
• B) \(-\frac{\left(x-\frac{\pi}{3}\right)^{3}}{12}\)
• C) \(\frac{\sqrt{3}\left(x-\frac{\pi}{3}\right)^{3}}{12}\)
• D) \(-\frac{\sqrt{3}\left(x-\frac{\pi}{3}\right)^{3}}{12}\)

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Definitions:

Zero-coupon Bonds

Bonds that do not pay periodic interest payments and are instead issued at a deep discount to their face value, maturing at par.

Treasury Bill

A Treasury Bill (T-Bill) is a short-term government debt obligation backed by the Treasury Department with a maturity of one year or less.

Par Value

The nominal or face value of a bond, share of stock, or coupon as indicated on a certificate or instrument.

Effective Annual Yield

The return on an investment expressed as an annual rate, taking into account the effect of compounding interest.