Let
![g(x)=ax^2+bx+c](https://tex.z-dn.net/?f=g%28x%29%3Dax%5E2%2Bbx%2Bc)
. Then
![\begin{cases}g(0)=c\\g'(0)=b\\g''(0)=2a\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dg%280%29%3Dc%5C%5Cg%27%280%29%3Db%5C%5Cg%27%27%280%29%3D2a%5Cend%7Bcases%7D)
Meanwhile, since
![f(x)=e^x](https://tex.z-dn.net/?f=f%28x%29%3De%5Ex)
, you have
![f(0)=f'(0)=f''(0)=e^0=1](https://tex.z-dn.net/?f=f%280%29%3Df%27%280%29%3Df%27%27%280%29%3De%5E0%3D1)
.
It follows that
![a=\dfrac12](https://tex.z-dn.net/?f=a%3D%5Cdfrac12)
,
![b=1](https://tex.z-dn.net/?f=b%3D1)
, and
![c=1](https://tex.z-dn.net/?f=c%3D1)
, so that the quadratic fit for
![f(x)=e^x](https://tex.z-dn.net/?f=f%28x%29%3De%5Ex)
that satisfies the given points is
![g(x)=\dfrac12x^2+x+1](https://tex.z-dn.net/?f=g%28x%29%3D%5Cdfrac12x%5E2%2Bx%2B1)
Note that this is just the second-order Taylor polynomial for
![e^x](https://tex.z-dn.net/?f=e%5Ex)
about
![x=0](https://tex.z-dn.net/?f=x%3D0)
.
Answer:
4
Step-by-step explanation:
I believe but i also got 3.6
80x20=1600 costumes
12x90=1080 masks
1600-1080=520
they ordered 520 more costumes than masks. hope this helps!
Answer:
16:1
Step-by-step explanation:
The ratio of the surface areas of the similar solids is the square of the lengths.
(4:1)²
4²:1²
⇒ 16:1
Answer:
noooooo
Step-by-step explanation: