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2 years ago

Please helpsina×tga=1/2find cosa

Mathematics

1 answer:

ioda2 years ago

4 0

Step-by-step explanation:

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Use the Taylor series you just found for sinc(x) to find the Taylor series for f(x) = (integral from 0 to x) of sinc(t)dt based

Marina CMI [18]

In this question (brainly.com/question/12792658) I derived the Taylor series for $\mathrm{sinc}\,x$ about $x=0$ :

$\mathrm{sinc}\,x=\displaystyle\sum_{n=0}^\infty\frac{(-1)^nx^{2n}}{(2n+1)!}$

Then the Taylor series for

$f(x)=\displaystyle\int_0^x\mathrm{sinc}\,t\,\mathrm dt$

is obtained by integrating the series above:

$f(x)=\displaystyle\int\sum_{n=0}^\infty\frac{(-1)^nx^{2n}}{(2n+1)!}\,\mathrm dx=C+\sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)^2(2n)!}$

We have $f(0)=0$ , so $C=0$ and so

$f(x)=\displaystyle\sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)^2(2n)!}$

which converges by the ratio test if the following limit is less than 1:

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(-1)^{n+1}x^{2n+3}}{(2n+3)^2(2n+2)!}}{\frac{(-1)^nx^{2n+1}}{(2n+1)^2(2n)!}}\right|=|x^2|\lim_{n\to\infty}\frac{(2n+1)^2(2n)!}{(2n+3)^2(2n+2)!}$

Like in the linked problem, the limit is 0 so the series for $f(x)$ converges everywhere.

7 0

2 years ago

What is the equation in point-slope from for the line that passes through the points (-3,5) and (2,-3)?

Aleks [24]

Answer:

$y + 3 = -1\frac{3}{5}[x - 2]\:or\:y - 5 = -1\frac{3}{5}[x + 3]$

Step-by-step explanation:

First, find the rate of change [slope]:

$\frac{-y_1 + y_2}{-x_1 + x_2} = m$

$\frac{-5 - 3}{3 + 2} = -\frac{8}{5} = -1\frac{3}{5}$

Now input the slope into the Point-Slope Formula. In this formula, all negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT signs:

$y - y_1 = m[x - x_1]$

$y + 3 = -1\frac{3}{5}[x - 2]\:or\:y - 5 = -1\frac{3}{5}[x + 3]$

I am joyous to assist you anytime.

8 0

3 years ago

A coin is tossed two times. what is the probability of getting tails two times in a row?

goldfiish [28.3K]

It's a conditional probability: (We know that the probability of getting 1 tail or 1 head is equal to 1/2)

Probability ( Tail AND Tail) = 1/2 x 1/2 = 1/4

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3 years ago

Which theorem or postulate could be used to prove the congruence of the triangle?

I am Lyosha [343]

Answer:

S. S. S

By using this theorem.

5 0

2 years ago

Hipfecndonoeciewqoecneqcoqexoqw;?

kirza4 [7]

Answer:

jaksmjshebajkan slzns makjzblzisbbsljzbsnkdkx

6 0

3 years ago

Please helpsina×tga=1/2find cosa ​

Please helpsina×tga=1/2find cosa