is not necessarily 1, because .
The remarkable limit is .
Edit:
So the limit is 0.
Help with SOLVING!!! {LIMIT x -> 0+} sqrt(x) * e^(sin(pi/x))
I know the Limit is zero I want to know how. Here's what I got:
{LIMIT x -> 0+} sqrt(x) * e^(sin(pi/x)) (I assume continuity so i plug n chug)
{LIMIT x -> 0+} sqrt(0) * e^(sin(pi/0)) => {LIMIT x -> 0+} 0 * e^(sin(pi/x)) = INDETERMINATE
{LIMIT x -> 0+} sqrt(x) * e^((pi/x)*(sin(pi/x))/pi/x)) ({LIMIT x -> 0+} {LIMIT x -> pi/x+} (sin(pi/x))/pi/x) = 1)
{LIMIT x -> 0+} sqrt(x) * e^(pi/x) (I'm stuck here i plug in 0 for x and i get e^ (pi/0))