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
Hey
Width of the photo = 3"
Length of the photo = 5"
New length of the photo = 7 inches
Then
3/5 = x/7
5x = 7 * 3
5x = 21
x = 21/5
= 4.20 inches
Hoped I Helped
Multiply the price of the meal by the sales tax. Tips are added in after tax has been applied, so it would not be added in to calculate the tax.
Tax= Meal Cost * Tax %
=$80 * 7%
convert % to decimal (7% ÷ 100)
=80 * 0.07
=$5.60 sales tax paid
ANSWER: $5.60 was the sales tax the customer paid.
Answer:
<h2>2 and three-fourths </h2>
Step-by-step explanation:
Given the expression 
, the equivalent expression can be gotten as shown;
2 and three-fourth therefore gives the required expression
Answer:
$72.15
Step-by-step explanation:
x= pounds of steak
$
= money spent on steaks
If Neil buys 7.5 pounds of steak then x =7.5
$9.62(7.5) = $72.15
