New posts in Taylor Expansion

Using Taylor series expansion to solve the equation $\frac{\tanh^{-1}(x)}{\beta} -2x =0$

Find $ \lim\limits_{x\to \infty} \left(x-x^2 \ln (1+\frac{1}{x})\right) $ with Taylor

Applying the induction hypothesis indirectly? I have trouble understanding this proof.

How can I prove $\frac {d}{dx} {x^n} = n x^{n-1}$ for $ n \in \Bbb R$ without circular reasoning?

Prove the inequality $\frac{e^x+e^{-x}}{2} \leq e^{x^2/2}$ for all real numbers $x$.

Maclaurin expansion of $\arctan(x)/(1 − x).$

Asymptotics of the sum $\sum_{n=1}^\infty \frac{x^n}{n^n}$

Newtonian potential expansion identity

Maclaurin series for $\arctan^{2}(x)$

Solve the limit of the sucession $ \left(1+\frac{1}{2}\right) \left(1+\frac{1}{4}\right) \times \dots \times \left(1+\frac{1}{2^n}\right) $