Question

limit as n->infinity of (100-n)/(100+n)

Answer 1

I believe you are most likely missing a variable @staircasetoheaven

Answer 2

@staircasetoheaven Use the "Equation" button to type up the limit so it's more understandable. From what I see atm, seems as if you forgot to insert an 'x' unless that is actually the question.

Answer 3

I changed it, thanks :)

Answer 4

Notice that the function that we are taking a limit of is a rational function. Also notice the degree of both the numerator and denominator of this rational function is the same. As you might already know, the limit of as 'n' approaches infinity for any rational function whose denominator/numerator are of the same degree, then the limit is basically the horizontal asymptote which is the ratio of the leading coefficients of the top and bottom. I'll start by giving you an example:\[\bf \lim_{x \rightarrow \infty}\frac{ x^2+1 }{ x^2+6x+8 }\]Notice that the degree of is '2' of both the numerator and denominator, i.e. "2" is the highest exponent you see in the numerator and denominator. In such a situation, we simply take the ratio of the leading coefficients, i.e. the ratio of the coefficient of "x^2" in both. The top has a "1" in front of "x^2" and the bottom also has a "1" in front of x^2. So the ratio of the coefficients is 1. Hence:\[\bf \lim_{x \rightarrow \infty}\frac{ x^2+1 }{ x^2+6x+8 }=\frac{ 1 }{ 1 }=1\]

Answer 5

Now, from what I just told you, can you find the limit? @staircasetoheaven

Answer 6

is it -1

Answer 7

i think its -1 but my says its 1

Answer 8

yup, it is -1, you are actually correct.

Answer 9

It would be 1 if the expression were
(n-100)/(n+100).
Check for typo or wrong question.

Answer 10

i guess my book is wrong because i typed the problem correctly. Thanks everybody

Answer 11

@staircasetoheaven Good job. -1 is correct.

Answer 12

just adding on: @genius12 trick about leading coefficients can be made rigorous with either polynomial division or as a repeated application of l'Hopital's rule :-)