Question

6. lim (sin x)^{1/x} = 0 7-43 Find the limits. 7. lim_{x o 0} frac{e^x - 1}{sin x} 8. lim_{x o 0} frac{sin 2x}{sin 5x} 9. lim_{ heta o 0} frac{ an heta}{ heta} 10. lim_{t o 0} frac{te^t}{1 - e^t} 11. lim_{x o pi^+} frac{sin x}{x - pi} 12. lim_{x o 0^+} frac{sin x}{x^2} 13. lim_{x o +infty} frac{ln x}{x} 14. lim_{x o +infty} frac{e^{3x}}{x^2} 15. lim_{x o 0^+} frac{cot x}{ln x} 16. lim_{x o 0^+} frac{1 - ln x}{e^{1/x}} 17. lim_{x o +infty} frac{x^{100}}{e^x} 18. lim_{x o 0^+} frac{ln(sin x)}{ln( an x)} 19. lim_{x o +infty} xe^{-x} 20. lim_{x o pi^-} (x - pi) an frac{1}{2}x 21. lim_{x o +infty} x sin frac{pi}{x} 22. lim_{x o 0^+} an x ln x 23. lim_{x o pi/2^-} sec 3x cos 5x 24. lim_{x o pi} (x - pi) cot x 25. lim_{x o +infty} (1 - 3/x)^x 26. lim_{x o 0} (1 + 2x)^{-3/x} 27. lim_{x o 0} (e^x + x)^{1/x} 28. lim_{x o +infty} (1 + a/x)^{bx} 29. lim_{x o 1} (2 - x)^{ an[(pi/2)x]} 30. lim_{x o +infty} [cos(2/x)]^{x^2} 31. lim_{x o 0} (csc x - 1/x) 32. lim_{x o 0} (frac{1}{x^2} - frac{cos 3x}{x^2})

          6. lim (sin x)^{1/x} = 0
7-43 Find the limits.
7. lim_{x 	o 0} frac{e^x - 1}{sin x}
8. lim_{x 	o 0} frac{sin 2x}{sin 5x}
9. lim_{	heta 	o 0} frac{	an 	heta}{	heta}
10. lim_{t 	o 0} frac{te^t}{1 - e^t}
11. lim_{x 	o pi^+} frac{sin x}{x - pi}
12. lim_{x 	o 0^+} frac{sin x}{x^2}
13. lim_{x 	o +infty} frac{ln x}{x}
14. lim_{x 	o +infty} frac{e^{3x}}{x^2}
15. lim_{x 	o 0^+} frac{cot x}{ln x}
16. lim_{x 	o 0^+} frac{1 - ln x}{e^{1/x}}
17. lim_{x 	o +infty} frac{x^{100}}{e^x}
18. lim_{x 	o 0^+} frac{ln(sin x)}{ln(	an x)}
19. lim_{x 	o +infty} xe^{-x}
20. lim_{x 	o pi^-} (x - pi) 	an frac{1}{2}x
21. lim_{x 	o +infty} x sin frac{pi}{x}
22. lim_{x 	o 0^+} 	an x ln x
23. lim_{x 	o pi/2^-} sec 3x cos 5x
24. lim_{x 	o pi} (x - pi) cot x
25. lim_{x 	o +infty} (1 - 3/x)^x
26. lim_{x 	o 0} (1 + 2x)^{-3/x}
27. lim_{x 	o 0} (e^x + x)^{1/x}
28. lim_{x 	o +infty} (1 + a/x)^{bx}
29. lim_{x 	o 1} (2 - x)^{	an[(pi/2)x]}
30. lim_{x 	o +infty} [cos(2/x)]^{x^2}
31. lim_{x 	o 0} (csc x - 1/x)
32. lim_{x 	o 0} (frac{1}{x^2} - frac{cos 3x}{x^2})

$6. lim (sin x)^1/x = 0 7-43 Find the limits. 7. limx o 0 frace^x - 1sin x 8. limx o 0 fracsin 2xsin 5x 9. lim heta o 0 frac an heta heta 10. limt o 0 fracte^t1 - e^t 11. limx o pi^+ fracsin xx - pi 12. limx o 0^+ fracsin xx^2 13. limx o +infty fracln xx 14. limx o +infty frace^3xx^2 15. limx o 0^+ fraccot xln x 16. limx o 0^+ frac1 - ln xe^1/x 17. limx o +infty fracx^100e^x 18. limx o 0^+ fracln(sin x)ln( an x) 19. limx o +infty xe^-x 20. limx o pi^- (x - pi) an frac12x 21. limx o +infty x sin fracpix 22. limx o 0^+ an x ln x 23. limx o pi/2^- sec 3x cos 5x 24. limx o pi (x - pi) cot x 25. limx o +infty (1 - 3/x)^x 26. limx o 0 (1 + 2x)^-3/x 27. limx o 0 (e^x + x)^1/x 28. limx o +infty (1 + a/x)^bx 29. limx o 1 (2 - x)^ an[(pi/2)x] 30. limx o +infty [cos(2/x)]^x^2 31. limx o 0 (csc x - 1/x) 32. limx o 0 (frac1x^2 - fraccos 3xx^2)$

Added by Michael W.

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