GATE 2018 EC – Question 34
Taylor series expansion of $f(x)=\int_0^xe^{-\left(\frac{t^2}{2}\right)}dt$ around $x=0$ has the form
$$f(x)=a_0+a_1x+a_2x^2+\cdots$$
The coefficient $a_2$ (correct to two decimal places) is equal to ________.
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Correct answer: 0
Explanation
$e^{-t^2/2}=1-\frac{t^2}{2}+\cdots$, so $f(x)=x-\frac{x^3}{6}+\cdots$ has only odd powers. So the coefficient of $x^2$ is $a_2=0$.