Answer:
Slope of a tangent to the curve = ![f'(x) = \frac{-1 }{(x+1)^{2} }](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B-1%20%7D%7B%28x%2B1%29%5E%7B2%7D%20%7D)
Step-by-step explanation:
Given - y = 1/x+1
To find - Identify each expression that represents the slope of a tangent to the curve y=1/x+1 at any point (x,y) .
Proof -
We know that,
Slope of tangent line = f'(x) = ![\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}](https://tex.z-dn.net/?f=%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Bf%28x%2Bh%29%20-%20f%28x%29%7D%7Bh%7D)
We have,
f(x) = y = ![\frac{1}{x+1}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%2B1%7D)
So,
f(x+h) = ![\frac{1}{x+h+1}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%2Bh%2B1%7D)
Now,
Slope = f'(x)
And
![f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \\= \lim_{h \to 0} \frac{\frac{1}{x+h+1} - \frac{1}{x+1} }{h}\\= \lim_{h \to 0} \frac{x+1 - (x+h+1) }{h(x+1)(x+h+1)}\\= \lim_{h \to 0} \frac{x +1 - x-h-1 }{h(x+1)(x+h+1)}\\= \lim_{h \to 0} \frac{-h }{h(x+1)(x+h+1)}\\= \lim_{h \to 0} \frac{-1 }{(x+1)(x+h+1)}\\= \frac{-1 }{(x+1)(x+0+1)}\\= \frac{-1 }{(x+1)(x+1)}\\= \frac{-1 }{(x+1)^{2} }](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Bf%28x%2Bh%29%20-%20f%28x%29%7D%7Bh%7D%20%20%5C%5C%3D%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7B%5Cfrac%7B1%7D%7Bx%2Bh%2B1%7D%20%20-%20%5Cfrac%7B1%7D%7Bx%2B1%7D%20%7D%7Bh%7D%5C%5C%3D%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Bx%2B1%20-%20%28x%2Bh%2B1%29%20%7D%7Bh%28x%2B1%29%28x%2Bh%2B1%29%7D%5C%5C%3D%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Bx%20%2B1%20-%20x-h-1%20%7D%7Bh%28x%2B1%29%28x%2Bh%2B1%29%7D%5C%5C%3D%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7B-h%20%7D%7Bh%28x%2B1%29%28x%2Bh%2B1%29%7D%5C%5C%3D%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7B-1%20%7D%7B%28x%2B1%29%28x%2Bh%2B1%29%7D%5C%5C%3D%20%20%5Cfrac%7B-1%20%7D%7B%28x%2B1%29%28x%2B0%2B1%29%7D%5C%5C%3D%20%20%5Cfrac%7B-1%20%7D%7B%28x%2B1%29%28x%2B1%29%7D%5C%5C%3D%20%20%5Cfrac%7B-1%20%7D%7B%28x%2B1%29%5E%7B2%7D%20%7D)
∴ we get
Slope of a tangent to the curve = ![f'(x) = \frac{-1 }{(x+1)^{2} }](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B-1%20%7D%7B%28x%2B1%29%5E%7B2%7D%20%7D)
Answer:
I would say Yes, because they said he can but they passed a law that ignores the request of former Loyalist. So Abercrombie needs Confederation so they can help him get his property back.
I'm really sorry if this is bad I don't know any of this stuff so I just guess...
Answer:
5
Step-by-step explanation:
25 / ( 12-7) = 25 / 5 = 5
I hope im right!!
Answer: 1. No because there are no numbers to solve it. 2. Yes, has numbers. 3.Yes, has numbers. 4.No because there are no numbers to solve it. 5. not sure 6.not sure 7. not sure 8.not sure 9. not sure
Step-by-step explanation:
Answer:
ok
Step-by-step explanation: