Limits Properties

[Richardnm]

Hi there,

I just started studying calculus and I got an exercise like this: limit ((x+1)^(1/k)-1)/x as x ->0. I have the answer, is 1/k, but I don't understand if this is just coicidence ( I've tried with k=2 and k=3, factoring, it gives me 1/2 and 1/3, on that order). Does it relate to the fundamental limit
lim ((a^x)-1)/x=ln a as x->0 ?

Thanks

 

[Quaid]

I just started studying calculus and I got an exercise like this:

limit ((x+1)^(1/k))/x as x ->0

I have the answer, is 1/k, but I don't understand if this is just coicidence ( I've tried with k=2 and k=3, factoring, it gives me 1/2 and 1/3, on that order). Does it relate to the fundamental limit

lim ((a^x)-1)/x = ln a, as x->0 ?

Hi Richard:

The limit (as you've typed it) does not equal 1/k.

Please proofread your post, to ensure that you typed the function correctly.

Thanks