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Registered Member #19
Joined: Thu Feb 02 2006, 03:19PM
Location: Jacksonville, FL
Posts: 168
Hey everyone I'm stuck on these two problems that are part of my homework:
Find the limits of:
For the first problem I tried to evaluate the function as h approaches 0- but I end up with 0/0. So then I tried to rationalise the numerator but I get the same result. I wasn't even sure where to start with the second problem. I couldn't find any similar examples in my book.
Registered Member #19
Joined: Thu Feb 02 2006, 03:19PM
Location: Jacksonville, FL
Posts: 168
wrote ... im not at that lvel of math yet, but wouldn't that mean there are no limits?
0/0 means its indeterminate, which is we don't know anything about the limit. I can't use l'hopital's rule cause this is before the book goes into derivatives. So its assumed we don't know any calculus up to this point.
Registered Member #29
Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500
(1) -11/(2*sqrt(6)) (2) 2
If I am not mistaken. (2) can be solved by recognising that the leading term in the series representation of tan(t) = t (when t is "small). Hence 2t/tan(t) -> 2
The same thing can be done for (1). The first two terms in the series representation of the square-root term are
sqrt(5h^2+11h + 6) = sqrt(6) + 11h/(2sqrt(6))
Doing the sums, and you get the limit of -11/(2*sqrt(6))...
This is assuming you can use Taylor series representations in your assignment... L'hopital's rule makes life very easy...
Perhaps your teacher wants you to work from the basics of the "epsilon-delta" definition of the limit.....
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Math Homework Problem
