121^4-49
(11^2+7)(11^2-7) 1. 121. 49
11. × 11. 7 × 7
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!
There are the combinations that result in a total less than 7 and at least one die showing a 3:
[3, 3] [3,2] [2,1] [1,3] [2,3]
The probability of each of these is 1/6 * 1/6 = 1/36
There is a little ambiguity here about whether or not we should count [3,3] as the problem says "and one die shows a 3." Does this mean that only one die shows a 3 or at least one die shows a 3? Assuming the latter, the total probability is the sum of the individual probabilities:
1/36 + 1/36 + 1/36 + 1/36 + 1/36 = 5/36
Therefore, the required probability is: 5/36
Answer:
a^2+b^2=c^2
Step-by-step explanation:
You can apply this formula to any quadratic equation.
Answer:
Graph U
Step-by-step explanation:
A graph is used to illustrate the relationship between variables.
For graph U:
Graph U is positive on (-∞, ∞). The graph also increases on (-∞, ∞). The graph approaches 0 as x approaches -∞.
For graph V:
Graph V is positive on (-∞, ∞). The graph also increases on (-∞, ∞). The graph is negative as x approaches -∞.
For graph W:
Graph W is positive on (-∞, 0). The graph also increases on (-∞, 0). The graph approaches 0 as x approaches -∞.
For graph X:
Graph X is positive on (-∞, ∞). The graph also increases on (-∞, ∞). The graph is negative as x approaches -∞
For graph Y:
Graph Y is positive on (-∞, ∞). The graph also decreases on (-∞, ∞). The graph approaches 0 as x approaches ∞.
For graph Z:
Graph Z is negative on (-∞, ∞). The graph also decreases on (-∞, ∞). The graph is approaches 0 as x approaches -∞
