9β30 Find the limit or show that it does not exist. 9. lim_{x ? ?} rac{3x - 2}{2x + 1} 10. lim_{x ? ?} rac{1 - x^2}{x^3 - x + 1} 11. lim_{x ? -?} rac{x - 2}{x^2 + 1} 12. lim_{x ? -?} rac{4x^3 + 6x^2 - 2}{2x^3 - 4x + 5} 13. lim_{t ? ?} rac{?t + t^2}{2t - t^2} 14. lim_{t ? ?} rac{t - t?t}{2t^{3/2} + 3t - 5} 15. lim_{x ? ?} rac{(2x^2 + 1)^2}{(x - 1)^2(x^2 + x)} 16. lim_{x ? ?} rac{x^2}{?{x^4 + 1}} 17. lim_{x ? ?} rac{?{9x^6 - x}}{x^3 + 1} 18. lim_{x ? -?} rac{?{9x^6 - x}}{x^3 + 1} 19. lim_{x ? ?} (?{9x^2 + x} - 3x) 20. lim_{x ? -?} (x + ?{x^2 + 2x}) 21. lim_{x ? ?} (?{x^2 + ax} - ?{x^2 + bx}) 22. lim_{x ? ?} cos x 23. lim_{x ? ?} rac{x^4 - 3x^2 + x}{x^3 - x + 2} 24. lim_{x ? ?} ?{x^2 + 1} 25. lim_{x ? -?} (x^4 + x^5) 26. lim_{x ? -?} rac{1 + x^6}{x^4 + 1} 27. lim_{x ? ?} (x - ?x) 28. lim_{x ? ?} (x^2 - x^4) 29. lim_{x ? ?} x sin rac{1}{x} 30. lim_{x ? ?} ?x sin rac{1}{x}
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Find the limit or show that it does not exist: 9-30 3x^2 + 10 lim (2x + 1)/(4 + |4x^2 - 12|) lim (4Ε‘x + 6x^2 - 2) lim (4x^2 + 5)/(Ε‘x + 1) lim (20 - (27^2 + 31))/(2x^2 + 4x + 16) lim (x - 1)/(Ε‘x^2 + 2x + 1) lim (x + Ε‘(x^2 + 2x))/Ε‘(x + 4) lim (x + Ε‘(x^2 + ax + bx)) lim cos(x)/(Ε‘(3x^2 + x)) lim Ε‘(x^2 + 7x - 2)/(6 - Ε‘(x + 1) + Ε‘3) lim (x^3 + x^2)/(x + Ε‘(x^2 + x)) lim (x - 4)/(Ε‘(x + 4) - Ε‘(x - 1)) lim (x^2 + x)/(Ε‘(3x^2 + 5)) lim (x - 4)/(Ε‘(x + 1) + Ε‘(x - 3)) lim x*sin(1) lim sin(x)
Adi S.
6. lim (sin x)^1/x = 0 7-43 Find the limits. 7. lim (e^x - 1) / sin x, x->0 8. lim sin 2x / sin 5x, x->0 9. lim tan theta / theta, theta->0 10. lim te^t / (1 - e^t), t->0 11. lim sin x / (x - pi), x->pi+ 12. lim sin x / x^2, x->0+ 13. lim ln x / x, x->+inf 14. lim e^(3x) / x^2, x->+inf 15. lim cot x / ln x, x->0+ 16. lim (1 - ln x) / e^(1/x), x->0+ 17. lim x^100 / e^x, x->+inf 18. lim ln(sin x) / ln(tan x), x->0+ 19. lim xe^-x, x->+inf 20. lim (x - pi) tan 1/2x, x->pi- 21. lim x sin pi/x, x->+inf 22. lim tan x ln x, x->0+ 23. lim sec 3x cos 5x, x->pi/2- 24. lim (x - pi) cot x, x->pi 25. lim (1 - 3/x)^x, x->+inf 26. lim (1 + 2x)^(-3/x), x->0 27. lim (e^x + x)^1/x, x->0 28. lim (1 + a/x)^(bx), x->+inf 29. lim (2 - x)^tan[(pi/2)x], x->1 30. lim [cos(2/x)]^x^2, x->+inf 31. lim (csc x - 1/x), x->0 32. lim (1/x^2 - cos 3x / x^2), x->0
Andrew N.
29. Determine the infinite limit: lim(x + 2)/(x+ 2) 30. Determine the infinite limit: lim(x^2 - 9)/(x + 3) 31. Determine the limit: lim(x^2 - 1)/(x - 1) 32. Determine the limit: lim(5x^3 - 5)/(x - 5) 33. Determine the limit: lim(ln(x^2 - 9))/(7 - 3t) 34. Determine the limit: lim(cot(x))/(x^2 - 2x) 35. Determine the limit: lim(xcsc(x))/(x^2 + 0)
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