New posts in Taylor Expansion

How to prove this lower bound on $\log(1+x)$ for $x \geq 0$? How about $x > -1$?

Getting two very different answers for Maclaurin series for $xe^{x}$ - how is this possible?

Why using fewer terms of Taylor series doesn't give $0/0$ but gives a wrong answer?

What does it mean for a polynomial to be the 'best' approximation of a function around a point?

How do I show $(e^{x^2}-1)(e^{y^2}-1) \geq (e^{xy}-1)^2$ for all $x,y> 0$?

Taylor polynomial with remainder for solving limit

Prove $\sum_{n=0}^{\infty} \frac{\Gamma(n+(1/2))}{4^n(2n+1)\Gamma(n+1)}=\frac{\pi^{3/2}}{3}$

Find $\lim_{x\to 0^{+}} \frac{\theta(x)}{x}$

Prove integral inequality: $\int_{0}^{\frac{\pi}{2}}e^{\sin x}\,dx\geq\frac{\pi}{2}(e-1)$

Is there any geometrical intuition for the factorials in Taylor expansions?