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!
Both measurements are correct if you're rounding the dogs height.
But the more precise measurement would be 11 1/4.
Mainly because its a smaller fraction so it has more meaning to it instead of just plain 11
It would get more precise as the fraction got larger
For example.
Not very precise
11, 11 1/2, 11 1/4,
Precise
11 1/8, 11 1/16
Hope this helps!
Brainliest is always appreciated if you feel its deserved!<span />
Answer:
7
Step-by-step explanation:
7 =2 hx x e
Answer: No it's not
Step-by-step explanation:
1/3 x 6/1 = 6/3
6/3 = 2
Answer:
Let's solve for x.
y=12x
Step 1: Flip the equation.
12x=y
Step 2: Divide both sides by 12.
12x
/12
=
y
/12
x=
1
/12
y
Answer: x=
1
/12
y
Step-by-step explanation: Hope this helps :D
