CALCOLO DI LIMITI CON I LIMITI NOTEVOLI

E/O CONFRONTO DI INFINITI O INFINITESIMI

$$\lim_{x→+\infinity} \frac{2^x+\left(\frac{27}{10}\right)^x}{x+e^x}$$
$$\lim_{x→0}\,\frac{x\, \sin\,x\left(e^x-1\right)}{\ln\left({1+x}\right)\left(1-\cos\,x\right)}$$
$$\lim_{x→0^+}e^{-\frac{1}{x}}\left(e+2x\right)^{\frac{1}{x}}$$
$$\lim_{x→0}\left(\frac{\sin\,4x}{x}\right)^\frac{1}{x}$$
$$\lim_{x→+\infinity}\left(e^x-x^x\right)$$
$$\lim_{x→0}\frac{e^{x^2}-2+\cos\,x}{\sin^2x}$$
$$\underset{x\to 0}{\lim }\frac{\sqrt[5]{x+1}-1}{5x}$$
$$\underset{x\to 3}{\lim }\frac{\sqrt{x}-\sqrt{3}}{x-3}$$
$$\underset{x\to \mathrm{\infty }}{\lim }{\left(\frac{x-2}{x+2}\right)}^{x+6}$$
$$\underset{x\to \alpha }{\lim }\frac{\cos x-\cos \alpha }{x-\alpha }$$
$$\underset{x\to +\mathrm{\infty }}{\lim }\frac{\sqrt{1+x^2}}{4x-3}$$
$$\underset{x\to 0}{\lim }\frac{{(1+2x)}^5-1}{x}$$
$$\underset{x\to +\mathrm{\infty }}{\lim }\frac{\ln (2x^2+3)}{\ln (x^3-1)}$$
$$\underset{x\to \mathrm{\infty }}{\lim }{\left(\frac{\sqrt{2}x+4}{\sqrt{2}x-2}\right)}^{\frac{\sqrt{2}}{3}x+\sqrt{3}}$$
$$\underset{x\to 1}{\lim }\frac{x^2-1}{x^2+3x-4}$$
$$\underset{x\to 0}{\lim }\frac{3{\tan }^{2}x}{1-\cos x}$$
$$\underset{x\to 0}{\lim }\frac{\sin 2x}{x\cos x}$$
$$\underset{x\to \mathrm{\infty }}{\lim }{\left(\frac{x+\sqrt{3}}{x+2\sqrt{3}}\right)}^{-\frac{x}{\sqrt{3}}}$$
$$\underset{x\to 1}{\lim }\frac{x^3-x^2+x-1}{3x^2-8x+5}$$
$$\underset{x\to 0}{\lim }\frac{\sqrt{4-x}-\sqrt{x+4}}{x}$$