Thread: Finding the limit for an exponential. Removing discontinuities!!!!???

1. Finding the limit for an exponential. Removing discontinuities!!!!???

LIMIT x -> 0+ sqrt(x) * e(sin(pi/x))

2. Re: Finding the limit for an exponential. Removing discontinuities!!!!???

The exponential factor oscillates between 1/e and e, so the limit is simply 0.

3. Re: Finding the limit for an exponential. Removing discontinuities!!!!???

Originally Posted by kram19
LIMIT x -> 0+ sqrt(x) * e(sin(pi/x))
lim{x->0+} sqrt(x)*e^(sin(pi/x)) = lim{x->0+} sqrt(x)*e^(pi/x*sin(pi/x)/(pi/x)) = 0

Since lim{x->0+} sin(pi/x)/(pi/x) = 0

4. Re: Finding the limit for an exponential. Removing discontinuities!!!!???

Thank you fkf makes sense don't know why i didn't think of that.