Answer:
a square
Step-by-step explanation:
Let f(x) = p(x)/q(x), where p and q are polynomials and reduced to lowest terms. (If p and q have a common factor, then they contribute removable discontinuities ('holes').)
Write this in cases:
(i) If deg p(x) ≤ deg q(x), then f(x) is a proper rational function, and lim(x→ ±∞) f(x) = constant.
If deg p(x) < deg q(x), then these limits equal 0, thus yielding the horizontal asymptote y = 0.
If deg p(x) = deg q(x), then these limits equal a/b, where a and b are the leading coefficients of p(x) and q(x), respectively. Hence, we have the horizontal asymptote y = a/b.
Note that there are no obliques asymptotes in this case. ------------- (ii) If deg p(x) > deg q(x), then f(x) is an improper rational function.
By long division, we can write f(x) = g(x) + r(x)/q(x), where g(x) and r(x) are polynomials and deg r(x) < deg q(x).
As in (i), note that lim(x→ ±∞) [f(x) - g(x)] = lim(x→ ±∞) r(x)/q(x) = 0. Hence, y = g(x) is an asymptote. (In particular, if deg g(x) = 1, then this is an oblique asymptote.)
This time, note that there are no horizontal asymptotes. ------------------ In summary, the degrees of p(x) and q(x) control which kind of asymptote we have.
I hope this helps!
Answer:
³y+7-6x=16
Step-by-step explanation:
this is an example of a 3 evaluating expression equation. *I think*
So this is read as 23 degrees, 20 minutes, and 48 seconds. Each degree has 60 minutes and each minute has 60 seconds, somewhat like time. You must start from right to left for this to work. This may seem complicated but the way to find this is as follows:
23+(20+(48/60))/60. A simpler way to see this is by first taking 48/60 which is .8. Now you take 20+.8 which is 20.8 and you divide it by 60 once more. This comes out to be approximately .35. Now you have converted the seconds and minutes to degrees so you add 23+.35 which is 23.35. Therefore your answer is 23.35 degrees.
