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
dimaraw [331]
2 years ago
15

Use a Maclaurin series to obtain the Maclaurin series for the given function.

Mathematics
1 answer:
Rama09 [41]2 years ago
3 0

Answer:

14x cos(\frac{1}{15}x^{2})=14 \sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}

Step-by-step explanation:

In order to find this Maclaurin series, we can start by using a known Maclaurin series and modify it according to our function. A pretty regular Maclaurin series is the cos series, where:

cos(x)=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{2k}}{(2k)!}

So all we need to do is include the additional modifications to the series, for example, the angle of our current function is: \frac{1}{15}x^{2} so for

cos(\frac{1}{15}x^{2})

the modified series will look like this:

cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15}x^{2})^{2k}}{(2k)!}

So we can use some algebra to simplify the series:

cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15^{2k}}x^{4k})}{(2k)!}

which can be rewritten like this:

cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}

So finally, we can multiply a 14x to the series so we get:

14xcos(\frac{1}{15}x^{2})=14x\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}

We can input the x into the series by using power rules so we get:

14xcos(\frac{1}{15}x^{2})=14\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}

And that will be our answer.

You might be interested in
Please help! i really need to pass this
bagirrra123 [75]
Use the slope formula or since it's a straight line crossing the y axis at one, it means the y=1
8 0
3 years ago
Read 2 more answers
WRONG ANSWERS WILL BE REPORTED- PLS GIVE EXPLANATION WTIH ANSWER<br> 8TH GRADE MATH
raketka [301]

Answer:

95.

Step-by-step explanation:

2.85 times 10⁶=2850000

then 2850000÷30,000=9.5

so either 95 or 9.5

Which one sounds correct should be.

6 0
1 year ago
Read 2 more answers
A translation by_____ units to the right/left and _____ units up down
Alexandra [31]
8 units left and 5 units up
8 0
3 years ago
Read 2 more answers
Always ? Sometimes? Never <br> Explain
Stels [109]

Answer:

Sometimes

Step-by-step explanation:

Quadrilaterals are shapes with four sides.

This means some quadrilaterals will have 4 equal sides, others will have <em>no </em>equal sides!

There is no rule determining side length equivalence in quadrilaterals. But those may be sub-classified as other shapes.

6 0
2 years ago
A health researcher fund drive has raised 18,700 that is a 22% of the goal what is the goal
crimeas [40]
Hi !

<u /><span><u>A health researcher fund drive has raised 18,700 that is a 22% of the goal what is the goal ?
</u>
</span>
18,700 ↔ 22%
x ↔ 100%

x=\dfrac{100\times18,700}{22}\\\\\boxed{x=85,000}

The goal il 85,000.

4 0
3 years ago
Read 2 more answers
Other questions:
  • Janelle buys 4 cases of water , each case of water contains 12 bottles, janelle drinks 3 bottles of water, what expression repre
    6·2 answers
  • A rectangular room must have a maximum area of 84 square feet. If the room is to be 8 feet wide, what is the longest the room ca
    14·2 answers
  • Find the slope of the line that passes through (1, 4) and (10, 9). Simplify your answer and write it as a proper fraction, impro
    5·2 answers
  • If 8p = 3p + 25, what is the value of p? Select the best answer from the choices provided. p = 4 p = 5 p = 6 p = 8
    7·2 answers
  • Mary and Mia are assembling floor lamps. Mary can assemble 10 lamps per hour. Mia can complete 12 lamps per hour. Together, they
    13·1 answer
  • Practice: triangle sum theorem on a piece of paper solve for the variable , then find the missing angles
    14·1 answer
  • Write the equation for the line in the graph in y=mx+b form.
    10·1 answer
  • Look at the function below. f(x)=−x2−2x+8
    5·1 answer
  • Can someone like help with this pleasee
    8·1 answer
  • Please Helpppp!!!!! I Have no clue I forgot how to find the slope.
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!