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Esercizi di analisi matematica sui limiti

1. Limite $lim_{x to 0} frac{(cos(x))^{“tg”(x)} – 1}{x^3}$

2. Limite $lim_(xto 0)(logx-logtanx)/(1+x)^(1/x)$

3. Limite $lim_{x to +infty} (frac{x+2}{x+1})^x$

4. Limite $lim_{x to -infty} (frac{2x+3}{2x})^{1-x}$

5. Limite $lim_{x to +infty} x[(1 + frac{ln(10)}{x})^x – 10]$

6. Limite $lim_(x to pi/2){[cos(x/2)-sin(x/2)]*tanx}$

7. $lim_{xto 0}((log_{a}(x+2)-log_{a}(2))/x)$

8. Limiti sviluppo di Taylor $lim_{x to 0} frac{e^{“tg”^3(x)} – 1}{x (cos(x) – e^{x^2})}$

9. $lim_{x to +infty} root{3}{2 + x^3} – root{3}{1 + 2x^2 + x^3}$

10. $lim_{x to 0} frac{ln(1 + “arctg”(x))^x}{e – e^{cos^4(x)}}$

11. $lim_{x to +infty}sqrt{2 + x^3} – sqrt{1 + 2x^2 + x^3}$

12. Limiti notevoli e teorema di de l’Hopital $lim_{x to 0} frac{e – (1 + x)^{frac{1}{x}}}{x}$

13. Limite $lim_(xto -1)5^((x^2+1+2x)/(sin(x+1)))

14. Limite$lim_(xto pi/2)(cos2x+1)*tanx$

15. $lim_{x to +infty} frac{sin(frac{1}{x})}{sqrt{3x^2 + 1} – sqrt{3x^2 – 1}}$

16. Limite $lim_(xto 0)((sin^3x)/(1-cos^6x))$

17. $lim_{x to 0} frac{sin(ln(1-x))}{sin(x)}$