Determine whether f(x) approaches negative or positive infinity as x approaches 4 from the left and right.
f(x)= 1/(x-4)^2

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- anonymous

\[f(x)=\frac{ 1 }{ x-4^{2} }\]

- hartnn

you know what "x approaches 4 from left" mean?

- anonymous

In the negative direction, correct?

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## More answers

- hartnn

yes,
more precisely, it means
value of x is very very very near to 4 but LESS than 4
like 3.9 or 3.9999999

- anonymous

Okay, and from there I can come to the conclusion that it will be infinitely positive and infinitely negative as x approaches 4 from the left and right?

- hartnn

woah! slow down..
there are 2 cases there
when x approaches 4 from left,
then is x-4 negative or positive??
is (x-4)^2 negative or positive??
based on that you will be able to tell, whether its +infinity or -infinity

- hartnn

similarly, the other case
when x approaches 4 from right,
then is x-4 negative or positive??
is (x-4)^2 negative or positive??
based on that you will be able to tell, whether its +infinity or -infinity

- anonymous

from the right is positive infinity and from the left is negative infinity?

- hartnn

can you first answer these??
is x-4 negative or positive??
is (x-4)^2 negative or positive??

- anonymous

using what values? 3.999?

- hartnn

if you're consider x is approaching from left, then yes

- anonymous

then x-4 would be negative
(x-4)^2 is postive

- hartnn

good!
so for x approaching from left we get positive infinity :)

- hartnn

now take x approaching from right case

- anonymous

then it would be negative infinity

- anonymous

I understand now, sorry for not understanding it until now and thank you for helping me!

- hartnn

welcome ^_^

- hartnn

but actually for right case also, it will be +infinity

- hartnn

because (x-4)^2 will anyways be positive

- hartnn

- anonymous

im not that smart lol sorry

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