It works the same way if it begins negative, the negative in front of the 'x' terms just means that the hyperbola opens vertically.
'b' refers to distance from center to vertices in the 'y' direction because 'b' is with y term.
The vertices are at (0, +-4), b = 4
To find 'a' use the slope of the asymptotes.
slope = b/a = 4/a
Estimate slope by using a point that is farthest away from orgin, (10,20.5)
The asymptote will be slightly below the point (10,20)
This gives a slope of 20/10 = 2.
4/a = 2 ----> a = 4/2 = 2
Answer: a = 2, b = 4
Answer:
1 7/12
Step-by-step explanation:
Step-by-step explanation:
A Maclaurin series is a Taylor series that's centered at 0.
f(x) = ∑ₙ₌₀°° f⁽ⁿ⁾(0) / n! xⁿ
If we substitute f⁽ⁿ⁾(0) = (n + 1)!:
f(x) = ∑ₙ₌₀°° (n + 1)! / n! xⁿ
f(x) = ∑ₙ₌₀°° (n + 1) xⁿ
Use ratio test to find the radius of convergence.
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(n + 2) xⁿ⁺¹] / [(n + 1) xⁿ]│< 1
lim(n→∞)│(n + 2) x / (n + 1)│< 1
│x│< 1
R = 1
(-2.8)+0+(-2.6)+6.4
-2.8-2.6+6.4
-5.4+6.4
1