Re: Limits
- From: Passerby <passerby@xxxxxxxxxxxxxx>
- Date: Fri, 28 Dec 2007 01:00:59 -0500
On Thu, 27 Dec 2007 14:51:07 -0800 (PST), shapper <mdmoura@xxxxxxxxx>
wrote:
Hello,
I am looking for a few limits problems to give to my students.
I am looking for university level. I need complex limits. I am giving
them the L'Hopital rule:
http://en.wikipedia.org/wiki/Limit_(mathematics)#l.27H.C3.B4pital.27s_rule
Does anyone knows where can I get a few problems?
And does anyone knows a few free math eBooks for downloading?
Thanks,
Miguel
For your consideration:
(1 - x)^(1/x) as x -> 0
x / (x^2 + 1)^(1/2) as x -> oo
[cos(x) - cos(a)] / (x - a) as x -> a
(a^x - b^x) / x as x -> 0
log[cos(2 x)] / (pi - x)^2 as x -> pi
[tan(x) - x] / [x - sin(x)] as x -> 0
[sin(x) - x] / [x - tan(x)] as x -> 0
sec(3 x) / sec(5 x) as x -> pi/2
[1 - log(x)] / x as x -> 0
log(x - pi/2) / tan(x) as x -> pi/2
For all positive and negative values of n,
x^n / e^x as x -> oo
For all positive values of m and n,
[log(x)]^m / x^n as x -> oo
For all positive values of m and n,
x^n [log(x)]^m as x -> 0
1/(x - pi) - 1/sin(x) as x -> pi
x^x as x -> 0
x^(1/x) as x -> oo
(1 + a x)^(b/x) as x -> 0
[sin(x)]^tan(x) as x -> pi/2
Have the students study the limits toward the bottom of the page
<http://mathworld.wolfram.com/LHospitalsRule.html>
for examples where L'Hospital does not hold ... and why!
.
- References:
- Limits
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