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Mon 1 Aug, 2005 04:03 pm
I have two tough questions below. Can someone help me by atleast providing hints?
1) Find the limit of (x^4 + 5x^2 + 1) as x---> negative infinity.
2) Find the limit of x+3/sqrt{9x^2 -5x} as x---> negative infinity.
For question 2, do I have to rationalize the denominator?
1) I'd say was infinity (consider the equation as y = x^2) then question is limit of y^2 + 5y + 1 as y -> infinity
2) did you mean to type (x+3) / ... otherwise answer is -ve infinity + 3/infinity = -ve infinity + 0
Just remember x^2 swamps 5x so you can ask what happens to sqrt (9x^2) = 3x, so 3/3x converges approximating 1/x very quickly to +ve zero.
On the first one, you are taking a negative number to a positive power, so you end up with positive infinity.
The second one is a little better. Assuming you meant (x+3) in the numerator like G suggested, the three in the numerator becomes insignificant as does the -5x in the denominator. So this becomes x/sqrt(9x^2) = x/|3x|. So as x-> neg infinity, this becomes -1/3.
Here is an easy way to check yourself in the days of fancy calculators. Put in a number close to negative infinity. Say -1,000,000. You will get a number close to the answer. You can also do this as x->0 by putting in a very small number like 0.000001.
okay
I thank you for the hints and ideas.
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