What Are the Properties of Limits for Basic Functions?

[asdfsystema]

hey guys, thanks for taking the time to check over my answers !

lim h(x)= 0 lim f(x)= -5 lim g(x) = 9

1. lim h(x)+f(x)= -5
2. lim h(x)-f(x) = +5
3. lim h(x)*g(x)= 0
4. lim h(x)/f(x) = 0
5. lim h(x)/g(x)= 0
6. lim g(x)/h(x) = DNE
7. lim squareroot (f(x)) = DNE (?)
8. lim f(x)^-1 = -1/5 ?
9. lim 1/ f(x) - g(x) = -1/14?

Thanks in advance please help me check over my answers !

 

[Gib Z]

Yes, those are all correct. I am assuming you meant a brackets around the f(x) - g(x) on your last one. From the ?'s on your last 3 I am assuming you aren't too sure about them.

7. Does not exist as the Sqrt function is not defined in the neighborhood of -5.

8. It's just the same rule you used in 4, but this time its 1 instead of lim h(x) on the numerator.

9. Same rule again - Limit of the whole thing is limit of the top over the limit of the bottom. And the limit of the bottom just uses the rule you used in 2.

 

[asdfsystema]

thank you ! you're right =)