Solving Limits - Questions on x^(sinx) & (9^x)/(8^x)

[mad]

Hello, I have two questions concerning limits

1) lim x-> 0+ x^(sinx)
2) lim x-> +inf. (9^x)/(8^x)

The first one gives me 1 (e^0 = 1) .. is that correct?
The 2nd one I don't know how to do. Can someone please explain the 2nd one for me?
Thanks a lot

 

[Gokul43201]

1) Correct

2) (9^x)/(8^x) = (9/8)^x and 9/8 > 1. How does a^x behave if a<1, a=1, a>1 ?

 

[mad]

1) Correct

2) (9^x)/(8^x) = (9/8)^x and 9/8 > 1. How does a^x behave if a<1, a=1, a>1 ?

I knew it was that simple! Thanks for the help :)