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2 years ago

How many output points does the vertical line test cross in this graph, and is it a function?

Mathematics

1 answer:

GenaCL600 [577]2 years ago

3 0

Answer:

Step-by-step explanation:

12 output points

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Can I get help with finding the Fourier cosine series of F(x) = x - x^2

trapecia [35]

Assuming you want the cosine series expansion over an arbitrary symmetric interval $[-L,L]$ , $L\neq0$ , the cosine series is given by

$f_C(x)=\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos nx$

You have

$a_0=\displaystyle\frac1L\int_{-L}^Lf(x)\,\mathrm dx$
$a_0=\dfrac1L\left(\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{x=-L}^{x=L}$
$a_0=\dfrac1L\left(\left(\dfrac{L^2}2-\dfrac{L^3}3\right)-\left(\dfrac{(-L)^2}2-\dfrac{(-L)^3}3\right)\right)$
$a_0=-\dfrac{2L^2}3$

$a_n=\displaystyle\frac1L\int_{-L}^Lf(x)\cos nx\,\mathrm dx$

Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of

$\displaystyle\int(x-x^2)\cos nx\,\mathrm dx=\frac{(1-2x)\cos nx}{n^2}-\dfrac{(2+n^2x-n^2x^2)\sin nx}{n^3}$

and so

$a_n=-\dfrac{4L\cos nL}{n^2}+\dfrac{(4-2n^2L^2)\sin nL}{n^3}$

So the cosine series for $f(x)$ periodic over an interval $[-L,L]$ is

$f_C(x)=-\dfrac{L^2}3+\displaystyle\sum_{n\ge1}\left(-\dfrac{4L\cos nL}{n^2L}+\dfrac{(4-2n^2L^2)\sin nL}{n^3L}\right)\cos nx$

4 0

3 years ago

Estimate the sum.<br> 85<br> + 61.7

Slav-nsk [51]

Answer:

150

Step-by-step explanation:

Round 85 to 90 and 61.7 to 60

7 0

3 years ago

Read 2 more answers

9,10,12,x,20,25 find x the median is 14

boyakko [2]

Answer:

Step-by-step explanation:

8 0

1 year ago

Read 2 more answers

Question 5

Mice21 [21]

Answer:

The missing value is 2

Step-by-step explanation:

A direct variation satisfies the equation $y=kx$ .

Since the point (-18, 12) lies on this line, it must satisfy this equation.

$\implies 12=-18k$

$k=-\frac{12}{18} =-\frac{2}{3}$

Hence the equation of this line is $y=-\frac{2}{3}x$

Now we substitute x=-3 to find y.

$y=-\frac{2}{3}*-3=2$

Therefore the missing value is 2

4 0

3 years ago

After two people answer one of my questions, how do I give brainlyist to one of them?

grin007 [14]

Vas happenin!
Hope your day is going well

Once two people answer your question there at the top of the question that they answer should have a crown and the words mark the Brainliest. Then it will go yellow when you mark it and it will also give you points

6 0

3 years ago

Read 2 more answers