Limits Question

So the question is:

Find the limit as x approaches negative infinity for: ((2-x)^2)e^x

I am not sure whether I completely understand but can you not just say as x approaches negative infinity, e^x approaches 0 and so the limit = 0

Thanks for any help.

Reply 1

TeeEm

19

Original post by jurd1

So the question is:

Find the limit as x approaches negative infinity for: ((2-x)^2)e^x

I am not sure whether I completely understand but can you not just say as x approaches negative infinity, e^x approaches 0 and so the limit = 0

Thanks for any help.

in a nutshell absolutely correct

exponential decay kills algebraic growth ...

Reply 2

Kallisto

Entertainment Forum Helper

22

Did you mean this function?

2*(2 - x)^2*e^x

If that is the case, so the limit is 0, if

x \to

- infinity.

Just because the graph is approaching 0 by increasing negative values of x. Plot the graph and do the math!

(edited 9 years ago)

Reply 3

davros

16

Original post by jurd1

So the question is:

Find the limit as x approaches negative infinity for: ((2-x)^2)e^x

I am not sure whether I completely understand but can you not just say as x approaches negative infinity, e^x approaches 0 and so the limit = 0

Thanks for any help.

The limit is 0, but in showing that you are using the fact that the exponential function dominates over polynomial growth.

What sort of techniques are you expected to use - i.e. is this a formal analysis course or just a high school or methods course?

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