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Esercizi di analisi matematica sui limiti

1. $lim_{xto a}(sinx-sina)/(cosx-cosa)$

2. $lim_(x->0)((e^(x*lnx)-cosx)/(lnx^2-arctgx))$

3. Determinarele costanti reali $a$ e $b$ in modo che:$lim_{xto+infty}((x^2+1)/(x+1)-ax-b)=-2$

4. $lim_(x->pi)((cos+cos2x)/(x-pi)^2)$

5. $lim_(x->infty)((x*sin(1/x)-1)/(1/x^2))$

6. $lim_(x->pi/2)(2xtgx-pi/cosx)$

7. $lim_(x->infty)((x+2)/x)^((x^2-x)/(3x+2))$

8. $lim_(x->0)1/x[((n+x),(n))-1]$

9. $lim_{x to infty}(x-sqrt(x^2+3))/(x-sqrt(x^2+x-3))$

10. $lim_(x->2) frac{3x+1}{x-1}

11. $lim_(x->0)(1/x-1/(e^x-1))$

12. $lim_{x to 0} frac{sqrt{4 x^4 – 6x^6} -2x^2}{log^2(cos(x))}$

13. $lim_(x rightarrow 0) (1-sin2x)^(1/ln(1+5x))$

14. $lim_ (x->+infty) sqrt(|x^2-4x-5|) -x$

15. $lim_(x->0)[x(e^x-1)]/[sinx*ln(1+5x)]$

16. $lim_(x->pi/2)log((3+tan^2x)/(2+tan^2x))=log[prop/prop]$

17. $lim_{nrightarrowinfty}frac{1}{sqrt{n^2+1}-n}$

18. $lim_{nrightarrowinfty}sqrt{n^6+n^2+1}-nsqrt{n^4+2}=$

19. $lim_{nrightarrowinfty}frac{2^sqrt{n}}{2^n+3^n}=$

20. $lim_{nrightarrowinfty}frac{n^2+n+(-1)^n}{n^2-n+1}=$

21. $lim_{nrightarrowinfty}[2^n+1-2nsin(frac{1}{n})]=$

22. $lim_{nrightarrowinfty} n^2 sin(frac{1}{n}) sqrt{1-cos(frac{2}{n})}=$

23. $lim_{nrightarrowinfty}(sqrt{n^2+n+2}cdot n)$

24. $lim_{xrightarrow +infty}[x-3x^2log(1+frac{1}{x})]$

25. $lim_{xrightarrow 0^+} log xcdot log(1+frac{1}{log x})$

26. $lim_{nrightarrowinfty}sqrt{n^2+n}cdot[1-cos(frac{1}{n})]$

27. $lim_{x rightarrow -infty}frac{2x-5}{x^2+1}=$

28. $lim_{xto+infty}((8x^4+4x+1)/(4x^4+2x))$

29. $lim_{xto+infty]((7x^2-2x)/(x^3+2x+1))$

30. $lim_{xto+infty}((5x^3+3x^2+2x-1)/(x^2+3x))$

31. $lim_{x rightarrow -infty}frac{5x^3+8x^2+1}{7x^2+8}$

32. $lim_{xto+infty}((3x^2+5x-1)/(2x^2+8x))$

33. $lim_{xto 3}((x^2-4x+3)/(2x-6))$

34. $lim_{xto 1}((x^2-2x-1)/(x^2-1))$

35. $lim_{xto 2}((x^3-2x^2-x+2)/(x^2-5x+6))$

36. $lim_{xto 2}((x^2-4)/(x^2-3x+2))$

37. $lim_{x rightarrow -2}frac{x^3+2x^2+x+2}{x^3+6x^2+12x+8} =$

38. $lim_{xto-infty}((x^2+x+7)/(x^3+4x^2+1))$

39. $lim_{xto-infty}((x^3-2x^2+1)/(x^2+7x+5))$

40. $lim_{xto+infty}((2x^2+x+1)/(7x^2-x))$

41. $lim_{xto-infty}((4x^5+2x+3)/(2x^2+3x+1))$

42. $lim_{xto-infty}((x^3-5x+4)/(2x^3+5))$

43. $lim_{xto(1/2)}-(1/(2x-1)+(3+x)/(2x-1)^2)$

44. $lim_{xto 1}(1/(x-1)+1/(x^2-3x+2))$

45. $lim_{xto-2}((x+5)/(x+2)+(4-x)/(x^2+2x))$

46. $lim_{xto-4}(1/(2x+8)+4/(x^2-16))$

47. $lim_{x rightarrow 1^+} (frac{1}{x^2-1} + frac{1}{x^2-3x+2})$

48. $lim_{xto 1}((x^2-1)/(x^3-1))$

49. $lim_{xto 1}((x^5-4x^3+3)/(2x^3-3x^2+1))$

50. $lim_{xto 1}((x^2-3x+4)/(x^3-2x^2-3x+1))$