New posts in Limits Without Lhopital

Find: $\lim_{x→1}\frac{⁡Γ(1+x)Γ(2+x)⁡Γ(3+x)-12}{x-1}$

If $\lim_{x\to 0}{f(x)} = \lim_{x\to 0}{g(x)}=0$, then is $\lim_{x\to 0}\frac{\sin f(x)}{g(x)}= \lim_{x\to 0}\frac {f(x)} {g(x)}$?

Limit as $y\to x$ of $(\sin y-\sin x)/(y-x)$ without L’Hospital

Is 0 divided by a non-zero indeterminate equal to 0.

Evaluating $\lim_{x\to0}{\frac{\sqrt[3]{\cos{4x}}-\sqrt[3]{\cos{5x}}}{1-\cos{3x}}}$ without L'Hopital's rule

Calculate $\lim_{x\to \pi/4}\cot(x)^{\cot(4*x)}$ without L'Hôpital's rule

Elementary proof that $2^x$ is derivable

Evaluating $ \lim_{x\to \infty} x \left({{\left(\frac{x}{x+1}\right)}^{x}-\frac{1}{e}}\right)$

Evaluate $\lim_{n\to \infty}n\int_2^e{(\ln x)^n}dx$

Very indeterminate form: $\lim_{x \to \infty} \left(\sqrt{x^2+2x+3} -\sqrt{x^2+3}\right)^x \longrightarrow (\infty-\infty)^{\infty}$