Jika f(x) = 
-3x maka nilai dari
limit
h⇒0
adalah.......
a. 15 +10x
b. 15-10x
c. -5-10x
d. -3-10x
e. -3+10x
limit
h⇒0
adalah.......
a. 15 +10x
b. 15-10x
c. -5-10x
d. -3-10x
e. -3+10x
Takamori37
Jabarkan secara umum:
![$\begin{align}&=\lim_{h\to0}\frac{f(x)-f(x+10h)}{2h}\\&=\lim_{h\to0}\frac{(x^2-3x)-[(x+10h)^2-3(x+10h)]}{2h}\\&=\lim_{h\to0}\frac{x^2-3x-(x^2+20hx+100h^2-3x-30h)}{2h} \\ &=\lim_{h\to0}\frac{x^2-3x-x^2-20hx-100h^2+3x+30h}{2h} \\ &=\lim_{h\to0}\frac{30h-100h^2-20hx}{2h} \\ &=\lim_{h\to0}\frac{2h(15-50h-10x)}{2h} \\ &=\lim_{x\to0}15-50h-10x \\ &=15-50(0)-10x \\ &=\boxed{15-10x\ \ [B]}\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7D%26%3D%5Clim_%7Bh%5Cto0%7D%5Cfrac%7Bf%28x%29-f%28x%2B10h%29%7D%7B2h%7D%5C%5C%26%3D%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B%28x%5E2-3x%29-%5B%28x%2B10h%29%5E2-3%28x%2B10h%29%5D%7D%7B2h%7D%5C%5C%26%3D%5Clim_%7Bh%5Cto0%7D%5Cfrac%7Bx%5E2-3x-%28x%5E2%2B20hx%2B100h%5E2-3x-30h%29%7D%7B2h%7D+%5C%5C+%26%3D%5Clim_%7Bh%5Cto0%7D%5Cfrac%7Bx%5E2-3x-x%5E2-20hx-100h%5E2%2B3x%2B30h%7D%7B2h%7D+%5C%5C+%26%3D%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B30h-100h%5E2-20hx%7D%7B2h%7D+%5C%5C+%26%3D%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B2h%2815-50h-10x%29%7D%7B2h%7D+%5C%5C+%26%3D%5Clim_%7Bx%5Cto0%7D15-50h-10x+%5C%5C+%26%3D15-50%280%29-10x+%5C%5C+%26%3D%5Cboxed%7B15-10x%5C+%5C+%5BB%5D%7D%5Cend%7Balign%7D "$\begin{align}&=\lim_{h\to0}\frac{f(x)-f(x+10h)}{2h}\\&=\lim_{h\to0}\frac{(x^2-3x)-[(x+10h)^2-3(x+10h)]}{2h}\\&=\lim_{h\to0}\frac{x^2-3x-(x^2+20hx+100h^2-3x-30h)}{2h} \\ &=\lim_{h\to0}\frac{x^2-3x-x^2-20hx-100h^2+3x+30h}{2h} \\ &=\lim_{h\to0}\frac{30h-100h^2-20hx}{2h} \\ &=\lim_{h\to0}\frac{2h(15-50h-10x)}{2h} \\ &=\lim_{x\to0}15-50h-10x \\ &=15-50(0)-10x \\ &=\boxed{15-10x\ \ [B]}\end{align}")
2 votes
Thanks 1
bangbi
makasih om
Takamori37
Oke, sama-sama.
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