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Computing the limit directly:
![\displaystyle\lim_{h\to0}\frac{f(2+h)-f(2)}h=\lim_{h\to0}\frac{((2+h)^2+(2+h)+1)-7}h\\\displaystyle=\lim_{h\to0}\frac{5h+h^2}h\\=\displaystyle\lim_{h\to0}(5+h)=\boxed{5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bh%5Cto0%7D%5Cfrac%7Bf%282%2Bh%29-f%282%29%7Dh%3D%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B%28%282%2Bh%29%5E2%2B%282%2Bh%29%2B1%29-7%7Dh%5C%5C%5Cdisplaystyle%3D%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B5h%2Bh%5E2%7Dh%5C%5C%3D%5Cdisplaystyle%5Clim_%7Bh%5Cto0%7D%285%2Bh%29%3D%5Cboxed%7B5%7D)
Alternatively, you can recognize the limit as being equivalent the derivative of <em>f(x)</em> at <em>x</em> = 2, in which case differentiating and plugging in 2 gives
<em>f'(x)</em> = 2<em>x</em> + 1 => <em>f'</em> (2) = 5
One kiloliter is equal to one hundred dekaliters. Multiply
![9.43*100](https://tex.z-dn.net/?f=9.43%2A100)
to get your answer :)
Area of trapezoid:
A = 1/2(b1+b2)h
where
b1 = 30,
b2 = 28+12 = 40
Triangle FOG
a^2 = c^2 - b^2
a^2 = 13^2 - 12^2
a^2 = 169 - 144
a^2 = 25
a = √25
a = 5
FO = 5 so height h = FO = 5
Now you can find the Area of trapezoid
A = 1/2(b1+b2)h
A = 1/2(30 + 40) (5)
A = 1/2(70)(5)
A = 175
Answer
175 square units