How do you find the limit of ( 1 - (5/x) ) ^x as x approaches infinity?

1 Answer
Jun 7, 2016

the limit is : e^-5

Explanation:

the limit is of the form 1^∞

lim_(x->a) (f(x))^(g(x)) = lim_(x->a) ( 1 + ( f(x) - 1 ) )^( g(x) )

lim_(x->a) (f(x))^(g(x)) = e^(lim_(x->a) ( f(x) - 1 ) * (g(x))

hence,
In the question given, the limit is of the form : e^k

k = lim_(x->0) (-5/x)*(x)

k = -5

Therefore, the limit of the above function is : e^(-5)