# Limits w/ Lhopitals Urgent help:

• Mar 11th 2007, 09:42 AM
Limits w/ Lhopitals Urgent help:
http://rogercortesi.com/eqn/tempimagedir/eqn7579.png
Evaluate the lim
1.) No matter how I use Lhopital its always undefined because of the e
answer at the book for this is 0

2.) Helpp... this ones hard too...
• Mar 11th 2007, 10:44 AM
qbkr21
Re:

When situations such as these arrive. I mean ones you plug in the variable and the solution yields undefined; it's always a good habit to calculate the left and right hand limits by setting up a table. If a solution is said to be undefined it is because the the numbers at a certain point on the graph are heading in two totally different directions. You can see the work for problem one by clicking the link under #1. Keep in mind you can solve any limit problem by looking at a graph or setting up a table.

1.

http://item.slide.com/r/1/209/i/JXOn...E2Gsyds0QYUB_/

2.

I am still working on this problem. I know the answer is 0 because when you take the limit of both the left and right and side the number is limiting 0. I will keep you posted when I get the work.

Best of Luck!
• Mar 11th 2007, 12:50 PM
Soroban

I think I've got the first one . . .

Quote:

. . . . . e^{-1/x}
. lim . -----------
x→0+ . . . x

. . . . . . . . . . . . . . . . . . . . x^{-1} . . . . .
Rewrite the function: . lim . ---------- . . ---
. . . . . . . . . . . . . . . x→0+ .e^{1/x} . . . .

. . . . . . . . . . . . . . . . . . .-x^{-2} . . . . . . . . . . . . .1
Apply L'Hopital: . lim . -------------------- . = . lim . ---------- . = . 0
. . . . . . . . . . . .x→0+ -x^{-2}·e^{1/x} . . .x→0+ e^{1/x}