Question Detail

MTH 102 Practice Questions MTH 102 Objective Question

Question

The Maclaurin series expansion of cosh(x) is
Options
A 1+x²/2!+x⁴/4!+x⁶/6!+...
Correct Answer
B 1-x²/2!+x⁴/4!-x⁶/6!+...
C 1+x²/2+x⁴/4+x⁶/6+...
D x+x³/3!+x⁵/5!+x⁷/7!+...
Correct Answer

Option A is the correct answer.

Detailed Explanation

cosh x is the sum of ½(eˣ+e⁻ˣ), and its Maclaurin series is the even-power terms of eˣ's series with all positive signs: 1+x²/2!+x⁴/4!+x⁶/6!+...

Hint

cosh x is closely related to cos x's series but without the alternating signs.

Question Info