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:
Domain: x
8
Step-by-step explanation:
All real numbers minors than or equal to 8
Hope this helps
Answer:
(x^2-6)^2
Step-by-step explanation:
X=13/24 in decimal form it’s x=0.5416
Answer:
x = 3.6 cm
Step-by-step explanation:
By the theorem of intersecting secants,
"If two secants are drawn from a point outside the circle, product of the lengths of the secant segment and its external segment are equal."
3(3 + y) = 2(2 + 6 + 3)
9 + 3y = 2 × 11
3y = 22 - 9
3y = 13
y =
cm = 4.33 cm
Now we will apply theorem of intersecting chords to determine the value of x.
" When two chords intersect each other in a circle, product of their segments are equal"


cm
Therefore, x = 3.6 cm and y = 4.33 cm