Step-by-step explanation:
a) Use ratio test.
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[x²ᵏ⁺¹ / (2(k+1))!] / [x²ᵏ / (2k)!]│< 1
lim(n→∞)│[x²ᵏ⁺¹ / (2k+2)!] × [(2k)! / x²ᵏ]│< 1
lim(n→∞)│x (2k)! / (2k+2)!│< 1
lim(n→∞)│x / ((2k+2) (2k+1))│< 1
0 < 1
The interval of convergence is (-∞, ∞).
b) f(x) = ∑₎₍₌₀°° x²ᵏ / (2k)!
f'(x) = ∑₎₍₌₁°° 2k x²ᵏ⁻¹ / (2k)!
f'(x) = ∑₎₍₌₁°° x²ᵏ⁻¹ / (2k−1)!
f'(x) = ∑₎₍₌₀°° x²ᵏ⁺¹ / (2k+1)!
c) f(x) + f'(x) = ∑₎₍₌₀°° x²ᵏ / (2k)! + ∑₎₍₌₀°° x²ᵏ⁺¹ / (2k+1)!
Notice f(x) is the sum of even terms (2k) and f'(x) is the sum of odd terms (2k+1). Therefore:
f(x) + f'(x) = ∑₎₍₌₀°° xᵏ / k!
f(x) + f'(x) = eˣ
Here are some examples of equivalent ratios for 1/6:
2:12, 3:18, 4:24, 5:30, 6:36
All of these simplify to 1/6, which makes them equivalent. Hope this helps! :)
Correct question:
Every day Kim practice volleyball and clarinet each day she practices volleyball for 2.5 hours if after 8 days she practices both volleyball and the clarinet for a total of 36 hours how many hours per day did Kim practice clarinet.
Answer: 2 hours
Step-by-step explanation:
Everyday Kim practices volleyball and clarinet = v/ball + clarinet
Everyday volleyball practice = 2.5hours
That is clarinet(hours) + 2.5 hours of volleyball
After 8 day, total practice hours of both volleyball and clarinet equals 36 hours
The above information can be represented mathematically as thus:
Let h = hours per day of clarinet
8(h + 2.5) = 36
8h + 20 = 36
8h = 36 - 20
8h = 16
h = 16/8
h = 2
A little more than 8 days. If you divide 658 by 75 you should get the exact answer
