Answer:
All of them
Step-by-step explanation:
According to the ratio test, for a series ∑aₙ:
If lim(n→∞) |aₙ₊₁ / aₙ| < 1, then ∑aₙ converges.
If lim(n→∞) |aₙ₊₁ / aₙ| > 1, then ∑aₙ diverges.
(I) aₙ = 10 / n!
lim(n→∞) |(10 / (n+1)!) / (10 / n!)|
lim(n→∞) |(10 / (n+1)!) × (n! / 10)|
lim(n→∞) |n! / (n+1)!|
lim(n→∞) |1 / (n+1)|
0 < 1
This series converges.
(II) aₙ = n / 2ⁿ
lim(n→∞) |((n+1) / 2ⁿ⁺¹) / (n / 2ⁿ)|
lim(n→∞) |((n+1) / 2ⁿ⁺¹) × (2ⁿ / n)|
lim(n→∞) |(n+1) / (2n)|
1/2 < 1
This series converges.
(III) aₙ = 1 / (2n)!
lim(n→∞) |(1 / (2(n+1))!) / (1 / (2n)!)|
lim(n→∞) |(1 / (2n+2)!) × (2n)! / 1|
lim(n→∞) |(2n)! / (2n+2)!|
lim(n→∞) |1 / ((2n+2)(2n+1))|
0 < 1
This series converges.
Answer:cam
Step-by-step explanation:
Answer:
m = 
Step-by-step explanation:
I'm assuming by m, you mean the slope.
You have two points. (-11, 5) and (2, -4)
- m = change in y-value ÷ change in x-value
1) Substitute in the points.
m = 
2) Solve.
So, the slope would equal .
If the functions are inverses, then f(g(x)) = x.
A.
The functions are inverses of each other.
B. The domain of f(x) = x≠3. The domain of g(x) is x≠0.
The domain of f(g(x)) is (-∞, 0) ∪ (0, ∞).
The domain of g(f(x)) is (-∞, 3) ∪ (3, ∞).
<span>A diagonal cross section of a sphere produces a circle.
Regardless of how the sphere is cut, it will form a circle.
</span>
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