Help with Limits
- Thread starter helpme99
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pka
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- Jan 29, 2005
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The way you post this makes it seem as though you expect to be given the answer.
I truly hope not, because that is not the way we work.
Please tell us what you can do towards working this for yourself.
Tell us what it is that you do understand. Then ask for help starting from there.
HallsofIvy
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- Jan 27, 2012
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Do you not know any of the "principles of limits"?
Just about any textbook, after it introduces the definition of limits, quickly gives:
\(\displaystyle \lim_{x\to a} (f(x)+ g(x))= \lim_{x\to a} f(x)+ \lim_{x\to a} g(x)\)
\(\displaystyle \lim_{x\to a} (f(x)- g(x))= \lim_{x\to a} f(x)- \lim_{x\to a} g(x)\)
\(\displaystyle \lim_{x\to a} (f(x)g(x))= \left(\lim_{x\to a} f(x)\right)\left(\lim_{x\to a} g(x)\right)\)
\(\displaystyle \lim_{x\to a} \frac{f(x)}{g(x)}= \frac{\lim_{x\to a} f(x)}{\lim_{x\to a} g(x)}\)
provided \(\displaystyle \lim_{x\to a} g(x)\ne 0\)
Those very easily give you the solution to this problem.
Just about any textbook, after it introduces the definition of limits, quickly gives:
\(\displaystyle \lim_{x\to a} (f(x)+ g(x))= \lim_{x\to a} f(x)+ \lim_{x\to a} g(x)\)
\(\displaystyle \lim_{x\to a} (f(x)- g(x))= \lim_{x\to a} f(x)- \lim_{x\to a} g(x)\)
\(\displaystyle \lim_{x\to a} (f(x)g(x))= \left(\lim_{x\to a} f(x)\right)\left(\lim_{x\to a} g(x)\right)\)
\(\displaystyle \lim_{x\to a} \frac{f(x)}{g(x)}= \frac{\lim_{x\to a} f(x)}{\lim_{x\to a} g(x)}\)
provided \(\displaystyle \lim_{x\to a} g(x)\ne 0\)
Those very easily give you the solution to this problem.