+0  
 
0
461
11
avatar+1832 

 Nov 26, 2014

Best Answer 

 #7
avatar+27396 
+15

L'Hopital

But I'm willing to be set straight!

 

NB: The last expression still reduces to e-5, so L'Hopital's rule still works of course, but I see it as an unnecessarily complicated approach here.

.

 Nov 27, 2014
 #1
avatar+27396 
+10

exponential limit

.

 Nov 26, 2014
 #2
avatar+1832 
0

Can you solve it by taking the lin in the both sides 

 Nov 26, 2014
 #3
avatar+27396 
+10

xvxvxv wrote: Can you solve it by taking the lin in the both sides 

 

I don't understand what you are asking!

.

 Nov 26, 2014
 #4
avatar+95375 
+10

Thanks Alan - I didn't know that 'by definition' bit.  

Actually you haven't used L'hopitals rule though ?  

 Nov 27, 2014
 #5
avatar+27396 
+10

In this case L'Hopital's rule makes things ten times worse!

.

 Nov 27, 2014
 #6
avatar+1832 
0

But we didn't study this method 

We always try to simplify it ti give us zero by zero or infinity by infinity then using l hopital rule 

 Nov 27, 2014
 #7
avatar+27396 
+15
Best Answer

L'Hopital

But I'm willing to be set straight!

 

NB: The last expression still reduces to e-5, so L'Hopital's rule still works of course, but I see it as an unnecessarily complicated approach here.

.

Alan Nov 27, 2014
 #8
avatar+95375 
+10

Hi Alan,

Yes I did not think that L'Hopital's rule helped either.

I was just pointing out that the question requested it and it was not used.  That is all.   :)

 Nov 27, 2014
 #9
avatar+1832 
0

Nice thank you Alan.  

But can you please explain to me your method 

First what do you mean by

" As t tend to infinity t+2 tends to t " 

 Nov 27, 2014
 #10
avatar+27396 
+10

Compare 5/(t+2) with 5/t for various values of t:

 

t        5/(t+2)                  5/t

1          1.67                       5

10        0.42                       0.5

100     0.049                      0.05

1000   0.00499                  0.005

...

106    4.99999*10-6           5*10-6

1010  4.999999999*10-10  5*10-10

 

You can see that as t gets bigger, 5/(t+2) becomes closer and closer to 5/t, so it's in this sense that t+2 becomes more and more like t as t tends to infinity.

.

 Nov 27, 2014
 #11
avatar+1832 
+5

nice 

thank you 

 Nov 27, 2014

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