Calculus: Limits

[KidInkFan]

1. lim as h approaches 0 of the function: (x²+h)/(x+h² )

2. lim as x approaches 0 of the function: x²/|x|

These are for an online assignment and i just can't seem to understand them for 1) you are left w x²/x so does that mean the answer goes to positive infinity? As for 2) I'm not really sure what

The choices provided to answer the questions are:

A	1
B	0
C	+
D	4
E	2
F	Does Not Exist
G	3
H	None of the above Thank you for taking the time to help me out!!

 

[JeffM]

1. lim as h approaches 0 of the function: (x²+h)/(x+h² )

2. lim as x approaches 0 of the function: x²/|x|

These are for an online assignment and i just can't seem to understand them for 1) you are left w x²/x so does that mean the answer goes to positive infinity? Does the problem indicate that x is zero. If x is not zero, why do you think x² / x = infinity. It looks like x to me.

As for 2) I'm not really sure what Problem Problem 2 is harder. It is in fact sort of a trick question. The function does not exist at
x = 0 because division by 0 is not allowed. But the limit does exist because the limit is defined at x close to BUT NOT EQUAL to 0. Division by 0 is ruled out by the definition of a limit.

The choices provided to answer the questions are:

A	1
B	0
C	+
D	4
E	2
F	Does Not Exist
G	3
H	None of the above Thank you for taking the time to help me out!!

Hope this helps

 

[KidInkFan]

Thank you so much for your help!!!