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
BARSIC [14]
2 years ago
9

Find maclaurin series

Mathematics
1 answer:
Mumz [18]2 years ago
7 0

Recall the Maclaurin expansion for cos(x), valid for all real x :

\displaystyle \cos(x) = \sum_{n=0}^\infty (-1)^n \frac{x^{2n}}{(2n)!}

Then replacing x with √5 x (I'm assuming you mean √5 times x, and not √(5x)) gives

\displaystyle \cos\left(\sqrt 5\,x\right) = \sum_{n=0}^\infty (-1)^n \frac{\left(\sqrt5\,x\right)^{2n}}{(2n)!} = \sum_{n=0}^\infty (-5)^n \frac{x^{2n}}{(2n)!}

The first 3 terms of the series are

\cos\left(\sqrt5\,x\right) \approx 1 - \dfrac{5x^2}2 + \dfrac{25x^4}{24}

and the general n-th term is as shown in the series.

In case you did mean cos(√(5x)), we would instead end up with

\displaystyle \cos\left(\sqrt{5x}\right) = \sum_{n=0}^\infty (-1)^n \frac{\left(\sqrt{5x}\right)^{2n}}{(2n)!} = \sum_{n=0}^\infty (-5)^n \frac{x^n}{(2n)!}

which amounts to replacing the x with √x in the expansion of cos(√5 x) :

\cos\left(\sqrt{5x}\right) \approx 1 - \dfrac{5x}2 + \dfrac{25x^2}{24}

You might be interested in
You are running a consention stand at a concersion stand at a basketball game. you are selling hot dogs and sodas. Each soda is
Tanya [424]

Answer:

38

Step-by-step explanation:

8 0
3 years ago
Carl and Tamera want to compare their tests in math class. They have taken six tests. Should they use the mean, median or mode t
Roman55 [17]

Answer:

Mean

Step-by-step explanation:

I said mean because it would allow both Carl and Tamera to average their scores and compare one side by side rather than comparing 6 each which would just be time consuming and it seems like it wouldn't be any other choices.

7 0
2 years ago
A submarine changes its position by −7 meters every second. What is the change in the submarine's position after 300 seconds?
Hoochie [10]
If you take -7*300 is should equal  -2100
5 0
3 years ago
Read 2 more answers
The Simmons family and the Wright family each used their sprinklers last summer. The water output rate for the Simmons family's
gizmo_the_mogwai [7]

Answer:

y=25 and x=30.

Step-by-step explanation:

See picture

4 0
3 years ago
Read 2 more answers
A grocery store sells steak for $6.10 per pound. What would be the cost of 2 3/5<br> lb of steak?
Gnesinka [82]

Answer: The answer is $15.86

Step-by-step explanation: You would change 6.10 into a fraction, which is 61/10. Then you would mulitply that and that number as a decimal would be 15.86.

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which object has a mass of approximately 450 grams?
    13·2 answers
  • PLEASE HELP IM SO CONFUSED!!!
    13·2 answers
  • Which expression is equivalent to −2.1+(−5.9)+(−3.7) ?
    12·1 answer
  • The length of a classroom is 34 feet. What is this measurement in yards and feet?
    14·1 answer
  • What is the polynomial function of lowest degree with lead coefficient 1 and roots i, -2 and 2?
    8·2 answers
  • Help me solve this problem please
    6·1 answer
  • 21g = 84<br><br> A. g = 3<br><br> B. g = 4<br><br> C. g = 5
    9·2 answers
  • The owner of a small restaurant bought 75 kilograms of rice. Each week, the restaurant uses 4.5 kilograms of rice.
    10·1 answer
  • Please help me i need help bad
    7·1 answer
  • HELP PLEASE! WILL GIVE BRAINLESIT ​
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!