X = number of sweaters
175 - 55 > 12X
120 > 12X
10 > X
the most amount of sweaters he can buy is 10
When 2x-5=0, implies that at x=5/2 function has discontinuity.
Answer:4
Step-by-step explanation:
Length = 3 breadth
which means 256 = 8 breadth
breadth = 32
length = 96
pls mark me as brainliest!
Presumably, the limit is
![\displaystyle\lim_{h\to0}\frac{(x+h)^3-x^3}h](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B%28x%2Bh%29%5E3-x%5E3%7Dh)
Now, if you're familiar with the definition of the derivatives, you'll notice that this is the limit form of the derivative of the function
![f(x)=x^3](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E3)
, which you may also know to be
![3x^2](https://tex.z-dn.net/?f=3x%5E2)
. But let's assume you don't know that just yet, and that it's actually the result you intend to find.
Expand the numerator:
![\dfrac{(x+h)^3-x^3}h=\dfrac{(x^3+3x^2h+3xh^2+h^3)-x^3}h=\dfrac{3x^2h+3xh+h^3}h](https://tex.z-dn.net/?f=%5Cdfrac%7B%28x%2Bh%29%5E3-x%5E3%7Dh%3D%5Cdfrac%7B%28x%5E3%2B3x%5E2h%2B3xh%5E2%2Bh%5E3%29-x%5E3%7Dh%3D%5Cdfrac%7B3x%5E2h%2B3xh%2Bh%5E3%7Dh)
Now, when
![h\neq0](https://tex.z-dn.net/?f=h%5Cneq0)
, we can divide through by the lowest power of
![h](https://tex.z-dn.net/?f=h)
. We can do this because we're considering the limit as
![h](https://tex.z-dn.net/?f=h)
is *approaching* 0, and not when it actually takes on the value of
![h=0](https://tex.z-dn.net/?f=h%3D0)
.
![\dfrac{(x+h)^3-x^3}h=3x^2+3xh+h^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%28x%2Bh%29%5E3-x%5E3%7Dh%3D3x%5E2%2B3xh%2Bh%5E2)
Now, as
![h\to0](https://tex.z-dn.net/?f=h%5Cto0)
, we can see only the leading term remains, so that
![\displaystyle\lim_{h\to0}\frac{(x+h)^3-x^3}h=3x^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B%28x%2Bh%29%5E3-x%5E3%7Dh%3D3x%5E2)
as expected.