if we replace x on the e with 3x what is the limit? Could i get some tips?
#Limits
long silo
fluid kelp
if we replace x on the e with 3x what is the limit? Could i get some tips?
Are you talking about the limit of (e^(nx) - 1)/x as x -> 0? Let's see.
Suppose f(x) = e^(nx). Then our limit becomes:
(f(x) - f(0))/x, x -> 0
By the definition of derivative, that tend to f'(0):
(f(x) - f(0))/x -> f'(0), x -> 0
So, let's find f'(0).
f'(x) = ne^(nx)
f'(0) = n
So, the limit is equal to n. In case of e^(3x), that would be 3.
long silo
no derivative use
fluid kelp
no derivative use
Ah. Hm... What can you use, then?
fluid kelp
Can you use the limit definition of e, then?
long silo
yes
fluid kelp
Ah, fantastic.