Taylor Series Practice Problems Online

Determine the Taylor series for the function $f(x) = \sin(x)\cos(x) \text{ centered at } x = \pi.$

\sum_{n=0}^{\infty} \frac{(-1)^n (x - \pi)^{2n + 1}}{(2n + 1)!}

\sum_{n=0}^{\infty} \frac{(-4)^n (x - \pi)^{2n + 1}}{(2n + 1)!}

\sum_{n=0}^{\infty} \frac{(-4)^n (x - \pi)^{2n}}{(2n)!}

\sum_{n=0}^{\infty} \frac{(-1)^n (x - \pi)^{2n}}{(2n)!}

At $a = 0$ , what is the Taylor series expansion of

$\ln ( 1 + x ) ?$

1 - x + \frac{1}{2} x^2 - \frac{1}{3} x^3 + \frac{1}{4} x^4 + \ldots

1 + x + \frac{1}{2} x^2 + \frac{1}{3} x^3 + \frac{1}{4} x^4 + \ldots

x + \frac{1}{2} x^2 + \frac{1}{3} x^3 + \frac{1}{4} x^4 + \ldots

x - \frac{1}{2} x^2 + \frac{1}{3} x^3 - \frac{1}{4} x^4 + \ldots

At $a = 0$ , what is the Taylor series expansion of

$\frac{1}{(1-x)^2} ?$

1 + 2 x + 3 x^2 + 4 x^3 + 5 x^4 + \ldots

1 + x + x^2 + x^3 + x^4 + \ldots

1 - \frac{1}{2} x + \frac{1}{3} x^2 - \frac{1}{4} x^3 + \frac{1}{5} x^4 + \ldots

1 - 2 x + 3 x^2 - 4 x^3 + 5 x^4 + \ldots

Given the Maclaurin series expansion of $\exp(x^2)$ as $a_0 + a_1 x^1 + a_2 x^2 + \cdots ,$ what is the value of $a_0 + a_1 + a_2$ ?

Determine the first three non-zero terms of the Taylor series for $f(x) = \tan(x) \text{ centered at } x = \frac{\pi}{4}.$

1 + 2\left(x - \frac{\pi}{4}\right) + \left(x - \frac{\pi}{4}\right)^2

1 + 2\left(x - \frac{\pi}{4}\right) + 2\left(x - \frac{\pi}{4}\right)^2

1 + \sqrt{2}\left(x - \frac{\pi}{4}\right) + \left(x - \frac{\pi}{4}\right)^2

1 + \sqrt{2}\left(x - \frac{\pi}{4}\right) + 2\left(x - \frac{\pi}{4}\right)^2

Taylor Series