Asked by Kate
Find the limit.
lim x->0 (e^(6/x)+8x)^(x/2)
lim x->0 (e^(6/x)+8x)^(x/2)
Answers
Answered by
Steve
try using the binomial expansion. You will see that the expression is
e^(6/x)^(x/2) + (x/2)e^(6/x)^(x/2-1)(8x) + ...
= e^3 + 4x^2*e^3/e^(6/x) + ...
where all the rest of the terms ->0
so, the limit is e^3
e^(6/x)^(x/2) + (x/2)e^(6/x)^(x/2-1)(8x) + ...
= e^3 + 4x^2*e^3/e^(6/x) + ...
where all the rest of the terms ->0
so, the limit is e^3