1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
OleMash [197]
3 years ago
5

How do you do these three questions?

Mathematics
1 answer:
mrs_skeptik [129]3 years ago
7 0

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

You might be interested in
Anna is weighing packages she is going to mail. They weigh 15.6 ounces, 13.25 ounces, 8.6 ounces, 9.75 ounces, and 18.23 ounces.
ella [17]
Estimation- 16 plus 13 plus 9 plus 10 plus 18= 66 ounces
Exact- 65.43 ounces
6 0
2 years ago
Simplify the equation 3x-4+2=-2x-5+5x Down to its simplest form do not solve the equation
lana66690 [7]

Answer:

the answer is 6x-7

Step-by-step explanation:

3x-4+2-2x-5+5x

3x-7-2x+5x

3x-7-2x+5x=

6x-7

7 0
2 years ago
Read 2 more answers
√30 what is the square root of 30?
sukhopar [10]

Answer:

5.47 is the square root of 30

6 0
1 year ago
Read 2 more answers
All of the following are equivalent, except _____.<br><br> 2x + x<br> x(2 + 1)<br> 2x2<br> 3x
vagabundo [1.1K]
They are all equal except 2x2
7 0
3 years ago
Read 2 more answers
Write the following ratio using two other notations. 4 : 5
Fittoniya [83]

Answer: It can also be written as 4/5 as a fraction or 4 to 5

5 0
3 years ago
Other questions:
  • Which construction would you use to construct a right triangle with a compass and a straightedge?
    14·1 answer
  • Solve for x x + 47 = -23
    8·2 answers
  • Inequality in real world.
    11·1 answer
  • Larry harvested 4/5 of his crops already he is able to harvest 1/10 of the crops per day how many days will it take for Larry to
    8·1 answer
  • Determine the time needed to deliver 72 papers at a rate of 9 papers in 18 minuets
    12·1 answer
  • The two figures are proportional find the value of x
    12·1 answer
  • Mr. canton places 24 desks in 6 equal rows. how many is in each row?? is it 24 times 6
    11·2 answers
  • Use the identity below to complete the tasks:
    7·1 answer
  • HELP ME PLEASE RNNN FASTTT
    7·1 answer
  • Describe the relationship between the area of a parallelogram and the area of a triangle if they have the same base and the same
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!