Question

find the limit as x approaches 0 of (1-(100/x^2))/(1+(100/x^2))

Answer 1

\[\lim_{x \rightarrow 0}\frac{ 1- \frac{ 100 }{ x ^{2} }}{ 1+\frac{ 100 }{ x ^{2} } }\]

Answer 2

multiply by x^2/x^2 to clear those fractions if they annoy you

Answer 3

so then im left with \[\frac{ x ^{2}-100 }{ x ^{2}+100 }\] correct?

Answer 4

so far so good

Answer 5

could I substitute x for 0 and get -100/100 which is -1? or is there more simplifying required?

Answer 6

thats as simple as it gets ...

Answer 7

the other way we simply leave x^2 where it is at, and get (1-inf)/(1+inf) = -(inf/inf) = -1 as a lazy trial lol

Answer 8

Refer to the attachment from the Mathematica program.