sinx =1-\frac{1}{2} (x-\frac{\pi}{2} )^2+\frac{1}{24} (x-\frac{\pi}{2} )^4-\frac{1}{720} (x-\frac{\pi}{2} )^6+\frac{1}{40320} (x-\frac{\pi}{2} )^8+...

Step-by-step explanation:

given that f(x) = sin x

we have to find the Taylor series for that

$f(x) = sin x : f( = 1\\f'(x) = cos x :(f'\frac{\pi}{2})=0\\f"(x) = -sinx :f" (\frac{\pi}{2}) =-1\\f^4 (x) = -cosx : f^4 (\frac{\pi}{2}) =0$

and so on.

i.e. 2nd, 4th, 6th terms would be 0

and also 1st, 5th, 9th terms would be positive for f value and 3rd, 9th,... would be negative

Using the above we can write Taylor series as

$f(x) = f(a)+\frac{f'(a)}{1!} (x-\frac{\pi}{2}) +...+f^n(a) /n! (x- \frac{\pi}{2})^n+...$

$sinx =1-\frac{1}{2} (x-\frac{\pi}{2} )^2+\frac{1}{24} (x-\frac{\pi}{2} )^4-\frac{1}{720} (x-\frac{\pi}{2} )^6+\frac{1}{40320} (x-\frac{\pi}{2} )^8+...$

This is valid for all real values of x.

x ∈ $(-\infty, infty)$

3 0

3 years ago

Please see this and help me

zhenek [66]

0-1 is 2
2-3 is 6
4-5 is 5
6-7 is 1

you need to count for example all 2 and 3 , and add put it number under 2-3

4 0

3 years ago

What is 20% off of 35

vodomira [7]

An easy way to find the precentage to to tuen the precentage to a decimal, in this case 20%=0.2, now multiply 35 by 0.2

35x0.2=7!

So 20% of 35 is 7$!

Another way to solve is to take 10% of 35, which you can find by just movig over the decimal (35-$3.50) now just add it together! 3.5+3.5=7$!!

Hope I helped!

6 0

4 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%283%20%5Cfrac%7B2%7D%7B5%7D%20%20-%201%20%5Cfrac%7B3%7D%7B10%7D%20%29%20%5Cdiv%201%20%5Cfrac%

nata0808 [166]

Answer:

$\frac{3}{2}$

Step-by-step explanation:

$[\frac{2}{5}-\frac{3}{10}+(3-1)]\div 1\frac{2}{5}\\\\=(\frac{4}{10}-\frac{3}{10}+2)\div\frac{5+2}{5}\\\\=(\frac{1}{10}+2)\div \frac{7}{5}\\\\=(\frac{2\cdot10+1}{10})\div \frac{7}{5}\\\\=\frac{21}{10}\div \frac{7}{5}\\\\=\frac{21}{10}\times \frac{5}{7}\\\\=\frac{21\cdot5}{10\cdot7}\\\\=\frac{3}{2}$

7 0

3 years ago