Step-by-step explanation:
f(x) = 1 / (5 + x)
Divide top and bottom by 5.
f(x) = ⅕ / (1 + ⅕x)
f(x) = ⅕ / (1 − (-⅕x))
Write as a geometric series.
f(x) = ∑ₙ₌₀°° ⅕ (-⅕x)ⁿ
f(x) = ∑ₙ₌₀°° ⅕ (-1)ⁿ (⅕)ⁿ xⁿ
f(x) = ∑ₙ₌₀°° (-1)ⁿ (⅕)ⁿ⁺¹ xⁿ
Use ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(-1)ⁿ⁺¹ (⅕)ⁿ⁺² xⁿ⁺¹] / [(-1)ⁿ (⅕)ⁿ⁺¹ xⁿ]│< 1
lim(n→∞)│-1 (⅕) x│< 1
│x/5│< 1
│x│< 5
-5 < x < 5
If x = -5, ∑ₙ₌₀°° ⅕ (-1)ⁿ (⅕)ⁿ (-5)ⁿ = ∑ₙ₌₀°° ⅕ (1)ⁿ, which diverges.
If x = 5, ∑ₙ₌₀°° ⅕ (-1)ⁿ (⅕)ⁿ (5)ⁿ = ∑ₙ₌₀°° ⅕ (-1)ⁿ, which diverges.
The interval of convergence is therefore (-5, 5).
Answer:
y=-9/6x+1
Step-by-step explanation:
Slope=y2-y1/x2-x1
1) Find the slope of the line:
(-5-4)/(4+2)
2) Simplify:
m= -9/6
3) Now plug in the slope into point slope formula: (attached as picture)
(y-4)=-9/6(x+2)
4) Distribute -9/6 to x and 2:
y-4=-9/6x-3
5) Add 4 to both sides:
y=-9/6x+1
The last one CL because of the order
Answer:
Step-by-step explanation:
Height of the Cylinder=10 Inches
Diameter of the Cylinder =3 inches
- Radius=Diameter/2=3/2=1.5 Inches
Volume of a Cylinder
Since the water in the vase raises to 9/10 of the way:
Volume of Water in the Vase
Step-by-step explanation:
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The lowest rank of the class is unknown to us.
Let's say, it's x.
highest marks =2 × lowest rank + 7
=> 87 = 2x + 7 (this is the equation we gotta solve)
=> 87 - 7 = 2x
=> 2x = 80
=> x = 40
And x is the lowest rank of the class, so we got the required answer.
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it can be 17 since the denominators are in increasing order and 17 only fits in.
I'm looking for any other pattern that can be present here.