A quick calculs question:?

Question

What do you do when you have a limit going to infinity and the answer is zero multipied times infinity. What's the procedure for getting around that?

as the lim of my fxn went to infinity, half of the fxn went towards 0 and the other towards infinity.

Answer 1

You have to manipulate the problem so it is in the form 0/0 or infinity/infinity.

Answer 2

If you have f(x) = g(x)*h(x), and g(x) approaches 0 and h(x) approaches infinity, then you use L'Hospital's Rule to find the limit of f(x). But first you have to make a change in the formula. You can let k(x) = 1/h(x). Then you get a new formula for f(x): f(x) = g(x)/k(x). Since h(x) approaches infinity, k(x) will approach 0. So f(x) approaches the indeterminate form 0/0. L'Hospital's Rule tells you how to handle this, and get an exact value for the limit.

If you haven't learned L'Hospital's Rule yet, it would require a great deal of ingenuity to solve this kind of problem, more than is generally asked of a calculus student.

Answer 3

there is a method in calculus to get around this but i forgot what you call it (lagrange method maybe? i dont know) anyway, what you need to do is to algebraically manipulate the function that you are trying get the limit of so that when you take the limit you will get a 0/0 or infinity over infinity. when you get there you just need to take the derivative of the numerator and the denominator once then try the limit. you can repeatedly take the derivative until you get to a point where the limit is definite number. hope this helps

Answer 4

When evaluating a limit and one part of the functon goes to infinity and the other part goes to zero, it may be time to try l'hospital's rule.

In simplest terms Limit of two functions is equal the ratio of the derivatives. L'hospital's rule does have condition's it can only be applied when you have a limit that is infinity/infinity,zero/zero, and infinity/zero. When you have zero * infinity; try changing the function.

Example:

f(x)*g(x)=f(x)/[1/g(x)]=g(x)/[1/f(x)]

An example of L'hospital's rule in action is the limit of the function

[x^(-1)]*ln|x|

at first it appears that the limit is zero*infinity.

Step 1:

Kick [x^(-1)] to the bottom.

(ln|x|)/x

Now take the derivative of the top.

d/dx(ln|x|)=1/x

Now take the derivative of the bottom.


d/dx(x)=1

Now evaluate the limit:

The limit as x goes to infinity of [1/x]/1= zero/1=0

This method should work fo evaluating the limit of a function at any point as long as it fits the conditions.

I suggest searching for the internet for L'hospital's rule for a better explanation or checking the index of your calculus book.
I like this one:
http://mathworld.wolfram.com/LHospitalsRule.html

Answer 5

What specifically is the problem? The answer depends on the context, because there are different degrees of infinity and zero may or may not be exactly zero.

Please type the function you're taking the limit of, because it might help to see it. Also, I believe my calculator can do limits.

Answer 6

You have f(x) that approaches infinity and g(x) that approaches 0.

Change f(x)*g(x) to either of the following:
1/(1/f(x) )*g(x) becomes a limit of the form 0/0

OR f(x)/(1/(1/g(x) ) ) becomes a limit of the form infinity/infinity

Answer 7

i'm not quite sure what your asking... but if the answer is zero, than anything times it would still be zero

Answer 8

Try arrainging your problem to use L'Hospital's rule.