Functions: behavior of y=x^100/exp(x) as x incr. w/o bound

[thinker86]

What is the behavior of the following function as x increases without bound? y=x^100/exp(x).

I am completely stuck on this question but I was wondering if you could plug in a huge number for x?

 

[pka]

Is this the question \(\displaystyle \lim _{x \to \infty } \frac{{x^{100} }}{{e^x }}\)?
Are studying caculus?

 

[thinker86]

This is a sample question for a placement test and it is under the pre-calculus category. I have no idea how to do it.

 

[stapel]

This is a sample question for a placement tes.... I have no idea how to do it.

If you "have no idea how to do" this sort of exercise, then the placement test will measure this, and put you in (or before) the course in which you will learn "how to do it". :wink:

That's the purpose of a placement test: to help ensure that the student is placed appropriately. If you somehow find a way to fake your way through this topic of the test, you may find yourself placed in a course which is too advanced for your actual level of learning. This (almost uniformly) means that you will flunk the course, probably many times. :shock:

Rather than attempt to accomplish this dubious feat, it would be better to review what you have studied (to make sure you don't miss a question you "should" know), and then let the placement test do its job. :idea:

Have fun!

Eliz.

 

[thinker86]

Even if this is a calculus problem and even though it is for a placement test, I would still like to know how to do it. I want to be as prepared as possible for my placement test because I want to at least get into Calculus I. I do not want to pay a bunch of money to take pre-calculus over when I already took it and did well in it. I know that I am prepared to take Calc I. There are a couple questions on the tests that were not covered in my pre-calc class and that is why I am asking this question. Can anyone help me figure it out?

 

[tkhunny]

Without the tools of calculus, you just have to play with it.

\(\displaystyle x^{100}\) This is big for relatively small x > 0.

\(\displaystyle e^{x}\) This gets really big, too. I wonder which one outpaces the other.

Note: Don't forget to look out past x = 100 before you make up your mind.

It is one of the purposes of calculus to give you an idea how to deal with such problems more easily. It would be good to have some idea about this one before you get there. Computer programmers know the difference between polynomial time and exponential time. There is a rule of thumb.

As was stated before, a placement test is intended to place you where it seems appropriate. If you magically get things right, things you don't actually know about, will that be telling the truth to the placement test?

 

[pka]

Even if this is a calculus problem and even though it is for a placement test, I would still like to know how to do it.

Frankly, there is no way to explain how one does this problem without knowing basic calculus. If you could understand the reasoning behind answer, then you don’t basic calculus.

I want to be as prepared as possible for my placement test because I want to at least get into Calculus I. I do not want to pay a bunch of money to take pre-calculus over when I already took it and did well in it. I know that I am prepared to take Calc I.

You are going to waste time and money if you do not pass calculus and are forced to take pre-calculus before you are allowed to take calculus again. Many, many schools have that policy. That is the purpose of the placement test.