• Support PF! Buy your school textbooks, materials and every day products Here!

The behaviour of e^x near infinity and -infinity

  • Thread starter laura_a
  • Start date
  • #1
66
0

Homework Statement



I have done an integration and ended up with the result

[-c/2 * [e^(-2x)]] |^infinity_0 = 1
The solution is that c=2 so that means to me that e^(2x) must turn into minus 1 for it to equal 1... but I'm not sure.. I've got graphcalc so I've been staring at the graph and I figure that as x goes to infinity that e^x goes to 1... but not sure what to say when x goes to minus infinity?
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
47
You should remember the following properties of the exponential function:
  • [tex]\lim_{x \to +\infty} e^x = \infty[/tex]
  • [tex]\lim_{x \to -\infty} e^x = 0[/tex]
  • [tex]\lim_{x \to 0} e^x = 1[/tex] (actually, the exponential function is continuous in 0, so one could also just say [tex]e^0 = 1[/tex], which is logical since [itex]x^0 = 1[/itex] for any [itex]x \neq 0[/itex]).
 
Last edited:
  • #3
6
1
e^x goes to 1 as x goes to 0.
e^x goes to 0 as x goes to negative infinity
e^x goes to infinity as x goes to infinity (no limit)

Is that what you're after?
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,770
911

Homework Statement



I have done an integration and ended up with the result

[-c/2 * [e^(-2x)]] |^infinity_0 = 1
The solution is that c=2 so that means to me that e^(2x) must turn into minus 1 for it to equal 1... but I'm not sure.. I've got graphcalc so I've been staring at the graph and I figure that as x goes to infinity that e^x goes to 1... but not sure what to say when x goes to minus infinity?
Then you need a new calculator! e^x does not go anywhere near 1 as x goes to infinity.
If you must use a calculator, what is e^1000000? What is e^(-100000)?
 

Related Threads for: The behaviour of e^x near infinity and -infinity

Replies
1
Views
2K
Replies
6
Views
2K
Replies
0
Views
1K
Replies
0
Views
5K
Replies
7
Views
2K
  • Last Post
Replies
17
Views
14K
Replies
1
Views
771
Top