Question

Evaluate the limit using L'Hospital's rule if necessary
limit (1+3/x)^(x/7)
x->inf

Answer 1

@ranga

Answer 2

it isn't necessary. plug in infinity

Answer 3

how did you figure that it isn't necessary?

Answer 4

you use l'hopital's only if you have

0^0 , inf^inf , 0/0 or inf/inf


plugging in inf gives 1^inf = 1

Answer 5

i thought the l'hopital's need to be used if it's also 1^inf..
and i plugged the answer 1^inf, and the system marked it wrong

Answer 6

answer is just 1

Answer 7

^inf is redundant

Answer 8

i also did put in 1, but it says it's wrong

Answer 9

Ln((1+3/x)^(x/7))= x/7*Ln(1+x/3)
L'hopital
use f(x)=Ln(1+3/x) and g(x)=7/x as functions they both ->0
You'll get lim f(x)/g(x)= lim f'(x)/g'(x)= 3/7
So lim (1+3/x)^(x/7) = exp(3/7)

Answer 10

my bad

Answer 11

rip that medal off my neck

Answer 12

That's okay

Answer 13

Thanks

Answer 14

yw