Problem 1161 (difficulty: 4/10)

Determine the Taylor series of the function at the given point.

(a) \(\displaystyle \displaystyle\frac1{1-x}\) at \(\displaystyle 0\);

(b) \(\displaystyle \displaystyle\frac1{x^2}\) at \(\displaystyle 3\);

(c) \(\displaystyle \log x\) at \(\displaystyle 5\) körül;

(d) \(\displaystyle \sin x\) at \(\displaystyle \displaystyle\frac{\pi}3\);

(e) \(\displaystyle \log(x^2-1)\) at \(\displaystyle 2\);

(f) \(\displaystyle \displaystyle\arsh x^2\) at \(\displaystyle 0\);

(g) \(\displaystyle \arcth x\) at \(\displaystyle 2\).

Give intervals where the Taylor series converges to the function.

Give me another random problem!