Thread: How to show limit?

Could anybody help me with the following limit: ln(x^.25)/sin(x-1) as x goes to 0 from above. I am confused since ln of 0 is negative infinity. How do i do this?

Thanks for any help.

You are correct that as x approaches zero, the numerator will approach negative infinity. So the question relies on the denominator now. You need to see if the sign will change. Have you tried plotting it?

I plotted the equation and the denominator and the equation looks to go to infinity (how do i show this without graph) and the denominator varies between -1 and 1. could you pleasee explain what you mean by "You need to see if the sign will change".

Thanks for the reply

As x approaches zero, the denominator will approach a negative finite amount. If you have some numerator which approaches negative infinity then we have a negative over a negative giving a positive sign in the result. So it seems to me the answer is positive infinity.

ok that seems to make sense. Thank you grillage.