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
A sum of money was shared between George and Benjamin in a ratio of 3:4. if the sum of money was $56.00, how much did George get
dybincka [34]

None  cause i got it from him :D

8 0
3 years ago
Juan went to the store to buy a plant for his mother, but forgot to ask which kind to get. Out of 30 plants, eighteen of them ar
Luba_88 [7]

Answer:

Probability [Randomly choose plant Juan's mother want] = 3 / 5

Step-by-step explanation:

Given:

Total number of plant in store = 30 plants

Number of plant kind Juan's mother want = 18

Find:

Probability [Randomly choose plant Juan's mother want]

Computation:

Probability of an event = Number of favorable outcome / Total number of outcomes

Probability [Randomly choose plant Juan's mother want] = Number of plant kind Juan's mother want / Total number of plant in store

Probability [Randomly choose plant Juan's mother want] = 18 / 30

Probability [Randomly choose plant Juan's mother want] = 3 / 5

7 0
2 years ago
A Boston subway train traveling at constant speed traveled 10.1 miles in half an hour. What was the speed of the subway train?
Klio2033 [76]
Speed of the train : distance traveled / time of the travel = 10.1/(0.5)=<span>20.2 mph. Hope this helped!</span>
7 0
3 years ago
Read 2 more answers
I need help ASAP!!Please explain how to do the problem
hoa [83]

Answer:

i think its 30

Step-by-step explanation:

perimeter is the sides added together

8 0
2 years ago
Read 2 more answers
A basketball hoop witha circumference of 56.52 inches i need to find the diameter
MA_775_DIABLO [31]

Answer:

Exactly, It would be this: 8.99543738355 . But rounded is 9 or 8.99

5 0
2 years ago
Other questions:
  • jane walked 4/5 mile on monday on tesday she wwalked 1//2 of the distance she walked on monday how many miles she walked on tues
    6·2 answers
  • An employee earns $261 for 18 hours of work. Assuming he is paid by the hour, how much will he earn in 7 hours?
    11·2 answers
  • Write 2 4/7 as an improper fraction
    13·1 answer
  • 15% of 20 is what number?
    15·1 answer
  • Stephanie is twice as old as her sister Rosa. If Stephanie is 18 years old, how old is Rosa?
    9·2 answers
  • A= 2; b= 3; c= 4; d= 12
    13·2 answers
  • On Christian's shelf are:
    14·1 answer
  • Complete the missing exponent. 64 = 4
    6·1 answer
  • What do the 300 and 10 in the diagram represent….PLEASE I NEED HELP FAST
    10·1 answer
  • The table shows the admission prices for an amusement park.<br> Which graph shows this function?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!