Maclaurin’s series expansion of cosx is ______?
- cosx = 1 + x²/2!+x⁴/4!-x⁶/6! + ...
- cosx = 1 - x²/2!+x⁴/4!-x⁶/6! + ...
- cosx = 1 - x²/2!+x⁴/4!-x⁶/6! - ...
- None of these
Explanation
The Maclaurin series expansion of cos(x) is derived from its Taylor series expansion around x = 0:
cos(x) = 1 - x²/2! + x⁴/4! - x⁶/6! + ...
This series alternates signs and involves even powers of x, with factorials in the denominators.
The answer is cosx = 1 - x²/2! + x⁴/4! - x⁶/6! + ...
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