Question #2ca19
1 Answer
Explanation:
When trying to take the limit of an exponential function, we can convert it to an easier form by using logarithms.
#=lim_(x->oo)e^ln(x^(1/sqrt(x)))#
#=lim_(x->oo)e^(1/sqrt(x)ln(x))#
#=e^(lim_(x->oo)ln(x)/sqrt(x))#
where the last equality follows from the continuity of
Now we can evaluate the limit in the exponent and then substitute it back into the equation above. As a direct attempt at evaluating the limit produces an
#=lim_(x->oo)(1/x)/(1/(2sqrt(x))#
#=lim_(x->oo)2/sqrt(x)#
#=0#
Now that we have that limit, we can substitute it back into the exponent to get our result.
#=e^0#
#=1#
So
