lim (X2 - 1/X) X->0-i am taking the limits and vertical asymptotes and i cant really get them so i have several questions but i asked only one of...

Hi,

Just to share.  To key x to the
power of 2, usually we just key x^2 .

For your
question:

lim (X^2 - 1/X)
X->0-

Do you mean

Case 1:  (x^2
- 1)/x

or

Case 2:  (x^2  - 1/x) 
?

I have done both cases for you:

Case
1

Take a peek at what the graph (the green one) is like by clicking
on the first link I had provided at the bottom to appreciate it.

The
expression is:   (x^2 - 1)/x

For very small values of x
(0<x<1),  x^2 << 1

Hence the function
approximates to -1/x .

With small negative values of x (0-), the
expression becomes +infinity

Lim (x^2 -1)/x , 
x->0-   =
+infinity

___

Case 2:
(x^2  - 1/x)

For very small values of x (0<x<1),  x^2 
becomes practically negligible and the term -1/x dominates.

Again,
the expression approximates to just  -1/x

Lim (x^2  -
1/x) , x->0-   =
+infinity

CONCLUSION

In
either case, the answer is still +infinity

(Apologies any confusion
caused prior to this ammendment on 3/12)

Click on the
links below, whichever the case you intended, and appreciate the question. It's fun!
:)