finding limit x -> 0 +

[selkie]

its asking for limit x approaching 0 from the right (answer = 0), am I meant to simplify this in some way to let me plug in zero? It looks like Im supposed to rationalize, but then what?
Thanks.

 

[Deleted member 4993]

It looks like Im supposed to rationalize, but then what?

Have you done that? What did you get?

Please show us your work for us to understand your difficulty.

 

[Dr.Peterson]

View attachment 34122
its asking for limit x approaching 0 from the right (answer = 0), am I meant to simplify this in some way to let me plug in zero? It looks like Im supposed to rationalize, but then what?
Thanks.

Typically, unless you are doing something you've done before, it is not helpful to ask "then what?" before you've done anything. Rather, do something, and then ask "now what?"

I say that because there may be several things that MIGHT come next; you don't know until you see what happened on the first step.

When you're lost in the woods without a map, you don't plan what to do when you get over the next hill, except that you plan to look around and see what looks like a good thing to try. Each step brings you new information.

Having said that: From my experience with problems like this, I EXPECT that I'll be able to cancel something ... UNLESS that turns out not to be necessary!

 

[JeffM]

This is vaguely like Dr. Peterson’s idea.

Try a little numerical experimentation with a calculator. That will suggest that a POSSIBLE answer is zero and why that answer makes sense.

However to prove that answer makes sense, here is a hint

[math]y = \sqrt { \dfrac{1}{x} + 2} - \sqrt{\dfrac{1}{x}}.\\ \text {Let } u = \dfrac{1}{x} \implies y = \sqrt{u+2} - \sqrt{u}. [/math]