Find, from the first principles, the gradient function of:
2 answers:
F(x+h) = x+h, and f(x) = x
So, your limit is:
![\lim_{h \to 0} \frac{x+h - x}{h} = \lim_{h \to 0} \frac{h}{h}](https://tex.z-dn.net/?f=%20%5Clim_%7Bh%20%5Cto%200%7D%20%20%5Cfrac%7Bx%2Bh%20-%20x%7D%7Bh%7D%20%3D%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%20%5Cfrac%7Bh%7D%7Bh%7D%20%20%20)
Applying l'hopital's rule,
![\lim_{h \to 0} \frac{h}{h} = \lim_{h \to 0} \frac{1}{1} = 1](https://tex.z-dn.net/?f=%20%5Clim_%7Bh%20%5Cto%200%7D%20%20%5Cfrac%7Bh%7D%7Bh%7D%20%20%3D%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%20%5Cfrac%7B1%7D%7B1%7D%20%3D%201)
Giving a gradient of
1.
![\begin{aligned}f'(x) &= \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h} \\&= \lim_{h \to 0} \dfrac{(x+h) - x}{h} \\&=\lim_{h \to 0} \dfrac{h}{h} \\&=\lim_{h \to 0} (1) && (\text{\footnotesize since $h/h = 1$ for $h\ne 0$})\\&= 1\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Df%27%28x%29%20%26%3D%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cdfrac%7Bf%28x%2Bh%29%20-%20f%28x%29%7D%7Bh%7D%20%5C%5C%26%3D%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cdfrac%7B%28x%2Bh%29%20-%20x%7D%7Bh%7D%20%5C%5C%26%3D%5Clim_%7Bh%20%5Cto%200%7D%20%5Cdfrac%7Bh%7D%7Bh%7D%20%5C%5C%26%3D%5Clim_%7Bh%20%5Cto%200%7D%20%281%29%20%26%26%20%28%5Ctext%7B%5Cfootnotesize%20since%20%24h%2Fh%20%3D%201%24%20for%20%24h%5Cne%200%24%7D%29%5C%5C%26%3D%201%5Cend%7Baligned%7D)
h/h = 1 is valid for h ≠ 0. The limit does not care about h at 0; it only cares about the values around it.
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60/12=5 years
100%+6%=106%=1.06
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Answer:
A
Step-by-step explanation:
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answer::::: 9 . Is it true ?
Answer:
2(a-2)
Step-by-step explanation:
12 + 2a – 8 = 2a +12-8
= 2a-4
=2(a-2)
So, This question was asked 6 DAYS AGO and I´m pretty sure that its been answered so- ima just take the points-
thamks