Analysis: Limits, strictly increasing, differentiability

[Shackleford]

I've worked all of these out. I'm mostly confident I did them correctly, but I'm prone to overlook subtleties or counterexamples sometimes.

http://i111.photobucket.com/albums/n149/camarolt4z28/1ab-1.png

http://i111.photobucket.com/albums/n149/camarolt4z28/1gf2-1.png

 

[SammyS]

1. b is false.

Is f(x) positive ?

I'll look at the other problem soon.

 

[Shackleford]

1. b is false.

Is f(x) positive ?

I'll look at the other problem soon.

Oh. You're saying the limit could be negative infinity, too, not just positive infinity. That's true.

 

[SammyS]

Or, f(x) could alternate from large positive to large negative values as x → ∞.

 

[SammyS]

The second link looked OK to me.

 

[Shackleford]

The second link looked OK to me.

Good catch on (b). Thanks for the review!

 

[deluks917]

Its possible your professor wants you to write out your steps a bit more.

 

[Shackleford]

Its possible your professor wants you to write out your steps a bit more.

For which ones?