GATE EE 2024 Set 1 — Question 31
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Engineering Mathematics → Complex Variables → Taylor & Laurent Series
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Question
Consider the complex function . The coefficient of in the Taylor series expansion of about the origin is ______ (rounded off to 1 decimal place).
Correct answer
0 to 0
Solution
The function is an even function because:
Thus, the coefficient of is .
1. (even function)
2. (even function)
The Taylor series expansion of an even function about the origin contains only even powers of . Therefore, the coefficients of all odd powers of (including ) are zero.Thus, the coefficient of is .
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