Question

limit as x approaches 0+ of (x- 1/x^3)

Answer 1

This basically means you want to choose numbers to the right of 0 to plug intoy our function and test what answers you get. This one works out pretty nicely because of your numerator. So if I chose x = 1 to test, we would get 0/1 = 0. Now I wouldtest one more pointeven closerto x = 0. Once I do that, my graph will either shoot up or shoot down. So testing 1/2, I would get:
\[\frac{ \frac{ 1 }{ 2 }-1 }{ (\frac{ 1 }{ 2 })^{3} }= \frac{ \frac{ -1 }{ 2 } }{ \frac{ 1 }{ 8 } }= -4\]So we got closer to 0 and we went down. If you werent sure enough you could test another point like 1/4, but you can see this graph will just get more and more negative, meanign the limit from the right would be negative infinity. Thats all you really have to do for these problems, test a point or two close to the limit and see if the numbers get really high or really low.