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)!}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccos%28x%29%20%3D%20%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20%28-1%29%5En%20%5Cfrac%7Bx%5E%7B2n%7D%7D%7B%282n%29%21%7D)
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)!}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccos%5Cleft%28%5Csqrt%205%5C%2Cx%5Cright%29%20%3D%20%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20%28-1%29%5En%20%5Cfrac%7B%5Cleft%28%5Csqrt5%5C%2Cx%5Cright%29%5E%7B2n%7D%7D%7B%282n%29%21%7D%20%3D%20%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20%28-5%29%5En%20%5Cfrac%7Bx%5E%7B2n%7D%7D%7B%282n%29%21%7D)
The first 3 terms of the series are
![\cos\left(\sqrt5\,x\right) \approx 1 - \dfrac{5x^2}2 + \dfrac{25x^4}{24}](https://tex.z-dn.net/?f=%5Ccos%5Cleft%28%5Csqrt5%5C%2Cx%5Cright%29%20%5Capprox%201%20-%20%5Cdfrac%7B5x%5E2%7D2%20%2B%20%5Cdfrac%7B25x%5E4%7D%7B24%7D)
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)!}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccos%5Cleft%28%5Csqrt%7B5x%7D%5Cright%29%20%3D%20%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20%28-1%29%5En%20%5Cfrac%7B%5Cleft%28%5Csqrt%7B5x%7D%5Cright%29%5E%7B2n%7D%7D%7B%282n%29%21%7D%20%3D%20%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20%28-5%29%5En%20%5Cfrac%7Bx%5En%7D%7B%282n%29%21%7D)
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}](https://tex.z-dn.net/?f=%5Ccos%5Cleft%28%5Csqrt%7B5x%7D%5Cright%29%20%5Capprox%201%20-%20%5Cdfrac%7B5x%7D2%20%2B%20%5Cdfrac%7B25x%5E2%7D%7B24%7D)
51 so I hope that help you in the long turm
Answer:
what do u need help with?
Step-by-step explanation:
209/2 is 104.5, add 0.5 to once and take away 0,5 once so your left with 104 and 105 then 104+105=209 and they’re integers which are consecutive. :))
The equation x = -8 contains the two points (-8 , -3) and (-8 , 1) ⇒ 2nd answer
Step-by-step explanation:
Let us revise the equations of the horizontal and vertical lines
- The equation of a horizontal line passes through point (a , b) is y = b, because all points lie on the line have the same y-coordinate b
- If a line passes through two points have the same y-coordinates, then the line is horizontal
- The equation of a vertical line passes through point (a , b) is x = a, because all points lie on the line have the same x-coordinate a
- If a line passes through two points have the same x-coordinates, then the line is vertical
∵ The line contained the two points (-8 , -3) and (-8 , 1)
∵ The two points have the same x-coordinate = -8
- From the 4th note above
∴ The line is vertical
∵ The equation of a vertical line is x = the x-coordinate of any point
on the line
∵ The x-coordinate of the points on the line = -8
∴ The equation of the line is x = -8
The equation x = -8 contains the two points (-8 , -3) and (-8 , 1)
Learn more:
You can learn more about the equation of a line in brainly.com/question/2657284
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