Answer:
A
Step-by-step explanation:
Well considering how the graph looks, from the x-axis(0,0), the line(x) moves upwards on the left before itf(x) moves downwards on the right
Answer: 7&8
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
-2 + 3v = -23 >> -2 + 23 = -3v >> 21 = -3v >> v = -7
Answer:
$0.75 per song
Step-by-step explanation:
Given that the relationship between variable s and c is a proportional relationship, and is represented by the equation, c = 0.75s.
Where,
c = total costs
s = number of songs
The constant of proportionality, k, = 0.75.
Thus, 0.75 represents the cost per sing downloaded.
The answer is:
✔️$0.75 per song
By first principles, the derivative is
![\displaystyle\lim_{h\to0}\frac{(x+h)^n-x^n}h](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B%28x%2Bh%29%5En-x%5En%7Dh)
Use the binomial theorem to expand the numerator:
![(x+h)^n=\displaystyle\sum_{i=0}^n\binom nix^{n-i}h^i=\binom n0x^n+\binom n1x^{n-1}h+\cdots+\binom nnh^n](https://tex.z-dn.net/?f=%28x%2Bh%29%5En%3D%5Cdisplaystyle%5Csum_%7Bi%3D0%7D%5En%5Cbinom%20nix%5E%7Bn-i%7Dh%5Ei%3D%5Cbinom%20n0x%5En%2B%5Cbinom%20n1x%5E%7Bn-1%7Dh%2B%5Ccdots%2B%5Cbinom%20nnh%5En)
![(x+h)^n=x^n+nx^{n-1}h+\dfrac{n(n-1)}2x^{n-2}h^2+\cdots+nxh^{n-1}+h^n](https://tex.z-dn.net/?f=%28x%2Bh%29%5En%3Dx%5En%2Bnx%5E%7Bn-1%7Dh%2B%5Cdfrac%7Bn%28n-1%29%7D2x%5E%7Bn-2%7Dh%5E2%2B%5Ccdots%2Bnxh%5E%7Bn-1%7D%2Bh%5En)
where
![\dbinom nk=\dfrac{n!}{k!(n-k)!}](https://tex.z-dn.net/?f=%5Cdbinom%20nk%3D%5Cdfrac%7Bn%21%7D%7Bk%21%28n-k%29%21%7D)
The first term is eliminated, and the limit is
![\displaystyle\lim_{h\to0}\frac{nx^{n-1}h+\dfrac{n(n-1)}2x^{n-2}h^2+\cdots+nxh^{n-1}+h^n}h](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bh%5Cto0%7D%5Cfrac%7Bnx%5E%7Bn-1%7Dh%2B%5Cdfrac%7Bn%28n-1%29%7D2x%5E%7Bn-2%7Dh%5E2%2B%5Ccdots%2Bnxh%5E%7Bn-1%7D%2Bh%5En%7Dh)
A power of
in every term of the numerator cancels with
in the denominator:
![\displaystyle\lim_{h\to0}\left(nx^{n-1}+\dfrac{n(n-1)}2x^{n-2}h+\cdots+nxh^{n-2}+h^{n-1}\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bh%5Cto0%7D%5Cleft%28nx%5E%7Bn-1%7D%2B%5Cdfrac%7Bn%28n-1%29%7D2x%5E%7Bn-2%7Dh%2B%5Ccdots%2Bnxh%5E%7Bn-2%7D%2Bh%5E%7Bn-1%7D%5Cright%29)
Finally, each term containing
approaches 0 as
, and the derivative is
![y=x^n\implies y'=nx^{n-1}](https://tex.z-dn.net/?f=y%3Dx%5En%5Cimplies%20y%27%3Dnx%5E%7Bn-1%7D)