SOLUTION: Find the limits of the given function lim 1/x^2-81 as a. x-->9+ b. x-->9- c. x--> -9+ d. x-->-9- Please explain, thanks in advance

Question 325796: Find the limits of the given function lim 1/x^2-81 as
a. x-->9+
b. x-->9-
c. x--> -9+
d. x-->-9-
Please explain, thanks in advance
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

As

gets close to -9 from the right,

will be a negative number whose absolute value is going to be a little smaller than 9, hence

is going to be a little smaller than 81, and therefore

becomes a very small negative number. 1 divided by a very small negative number is a very large negative number.

Using similar logic:

As

gets close to -9 from the left,

becomes a very small positive number. 1 divided by a very small positive number is a very large positive number.

As

gets close to +9 from the left,

becomes a very small negative number. 1 divided by a very small negative number is a very large negative number.

As

gets close to +9 from the left,

becomes a very small positive number. 1 divided by a very small positive number is a very large positive number.

John

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