help with these limts!
Author
i''ve stubmeled across these two limits when i was doing my homework and i just had not idea how to continue. i would really appreciate if someone would hint me as to what i should do about those limits. I DO NOT WANT AN ANSWER, i want guidelines.
1.
lim (1+x^2)^(cot^2(x))
x->0
2.
lim ( (2x^2+2x-1)/(2x^2-3x-2) )^(3x+1)
x->infinity
did you try using the log rule to rearrange them?
if lim f(x) -> inf^inf or 0^0 or some combination,then transform it:
lim f(x) = e^(log (f(x))
Then eval lim(log (f(x)), and then solve for e^ of that.
if lim f(x) -> inf^inf or 0^0 or some combination,then transform it:
lim f(x) = e^(log (f(x))
Then eval lim(log (f(x)), and then solve for e^ of that.
Remember when your old math teacher used to tell you to never divide by the variable? Well, limits is one of the places you would want do 
I''m not saying it would apply directly in this instance, but if you multiply the top and bottom of a rational fuction by x-n, n being the degree of the denominator, you can eliminate the x''s in the denominator and not have to worry about dividing the whole function by 0 or &inf when you take the limit.
I''m not saying it would apply directly in this instance, but if you multiply the top and bottom of a rational fuction by x-n, n being the degree of the denominator, you can eliminate the x''s in the denominator and not have to worry about dividing the whole function by 0 or &inf when you take the limit.
Author
first, thanks for everybody.
second, i had to use the log rule (thanks sjelkjd), and then use Lopital rule. well...that was it.
funny thing though, the homework was to calculate 16 limits, they all took me 3 pages, where the last two (those i had the problem with) took the entire last page.
and...if you want to see the entire solution, i can post it, sort of "seal the topic".
[edited by - danz on October 29, 2002 1:41:58 PM]
second, i had to use the log rule (thanks sjelkjd), and then use Lopital rule. well...that was it.
funny thing though, the homework was to calculate 16 limits, they all took me 3 pages, where the last two (those i had the problem with) took the entire last page.
and...if you want to see the entire solution, i can post it, sort of "seal the topic".
[edited by - danz on October 29, 2002 1:41:58 PM]
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