New posts in Limits Without Lhopital

Euler Limit of $\frac{x^x-x}{1-x+\ln(x)}$ Without L'Hopital

How to evaluate $\lim _{x\to \infty }\left(\frac{x+3}{\sqrt{x^2-5x}}\right)^{x^2\sin\left(1/x\right)}$?

Limit at infinity of cubic roots and square roots without using conjugate $\lim_{x \to \infty} \frac{\sqrt[3]{x+2}}{\sqrt{x+3}}$

Limit of the exponential functions: $\lim_{x\to 0} \frac{e^x-e^{x \cos x}} {x +\sin x}$

limit of $(e^x-1)^{\frac{1}{x}}$ - Without L'hopital

Calculate the limit without using L'Hopital's Rule: $\lim\limits_{x \to 0} \frac{5x - e^{2x}+1}{3x +3e^{4x}-3}$

Is there a more efficient way of evaluating this limit?

A limit without invoking L'Hopital: $\lim_{x \to 0} \frac{x \cos x - \sin x}{x^2}$

Limit of $\left(x^{3} - 1\right)\left(x^{2} - 1\right)^{1/3} \over 5\ln\left(x\right)$ when $x\to1^{+}$

Find a limit without l'Hospital: $\lim_{x\to -\infty}\left(\frac{\ln(2^x + 1)}{\ln(3^x+ 1)}\right)$