use l'hospital's rule to find the limit:

1. lim (tan 2x)^x

x-> 0+

i got 1 using ln y, but im not sure if its right..

2. lim (1+ (a/x))^bx

x-> INFINITY

again i got 1...but am unsure

any help is appreciated...thanks!!

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- September 9th 2008, 03:23 PMskabaniL'Hospital's Rule
use l'hospital's rule to find the limit:

1. lim (tan 2x)^x

x-> 0+

i got 1 using ln y, but im not sure if its right..

2. lim (1+ (a/x))^bx

x-> INFINITY

again i got 1...but am unsure

any help is appreciated...thanks!! - September 9th 2008, 03:29 PM11rdc11
I think the second one is the number e but just looked at it real fast

- September 10th 2008, 07:39 AMMoo
Hello,

I get 1 too :)

Quote:

2. lim (1+ (a/x))^bx

x-> INFINITY

Thus and

Remember the rule

Therefore :

(by taking the logarithm and applying l'Hospital's rule)

(a little substitution can be done if t tends to )

Otherwise, applying the logarithm :

Then apply l'Hospital's rule...