At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
There is a rule for horizonal asymptotes, related to the degree of the num'r vs. the degree of the den'r. Does that sound familiar?
Yes, so it is horizontal because the denominator is bigger than the numerator
One way of viewing it is to plug in a very large number x :) and evaluate
Well, that isn't what makes it a HORIZONTAL asymptote. There are 2 cases where you get a horizontal asymyptote: deg num'r < deg den'r deg num'r = deg den'r
(x + 9) / (x^2 + 8x + 8) just pick x= 999
This is the first of those, so it gives a specific result. Think of it this way: for a BIG value of x, the den'r is going to be MUCH BIGGER than the num'r, so it will "take over". What will that do to the value of the rational expression?
Or graphically https://www.google.com/search?q=(x+%2B+9)+%2F+(x%5E2+%2B+8x+%2B+8)&oq=(x+%2B+9)+%2F+(x%5E2+%2B+8x+%2B+8)&aqs=chrome..69i57.658j0&sourceid=chrome&ie=UTF-8 Just zoom out and scroll to the right and you will zee that the asymptote is... :D
in the previous case the numerator's "degree" was bigger than the denominator's in this case is the other way around, notice the degree of the numerator is 1 and the denominator's degree is 2 so you do have a horizontal asymptote, what is it? well, is at y =0, or the x-axis
x/x^2 here is another example the x^2 will get very big very fast as you aproach big numbers like 100 100/10000 = very small number 1000/1000000= even smaller number and you could say number is so small it aproaches 0
so y = x
well the x-axis line is y = 0
I would say 0 :)
here another example |dw:1377815631899:dw|
Ahh okayy ! Thanks everyone !!