Engineering Mat...

The Fourier series for an even function f(x) is given by

Find the coefficient of x² in expansion of e^2x about 0

Calculate the coefficient a₀ of Fourier series for

By using a suitable Maclaurin series, find the sum to infinity of the following infinite series

\(\pi - \frac{{{\pi ^3}}}{{3!}} + \frac{{{\pi ^5}}}{{5!}} - \frac{{{\pi ^7}}}{{7!}} + \ldots \;\)

For the function f(x) = x³ – 10x² + 6, the linear approximation around x = 3 is

1 + x + x²/2 – x⁴/8 – x⁵/15 + … =

In the Taylor series expansion of e^x + sin x about the point x = π, the coefficient of (x – π)² is

The Fourier series to represent x-x² for –π ≤ x ≤ π is given by \(x - {x^2} = \frac{{{a_0}}}{2} + \mathop \sum \limits_{n = 1}^\infty {a_n}cosnx + \mathop \sum \limits_{n = 1}^\infty {b_n}sinnx\)

Which of the following is the correct expansion of x² + e^2x about 1?

The Fourier Sine series for an odd function f(x) is given by

\(f\left( x \right) = \mathop \sum \limits_{n = 1}^\infty {b_n}\sin \frac{{n\pi x}}{L}\)

The value of the coefficient b₂ for the function \(f(x) = \sin ax,\,\, - \pi < x < \pi \) is