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yanalaym [24]
2 years ago
8

1. Find the derivative with respect to x of x +1/x from first principle. ​

Mathematics
1 answer:
Murrr4er [49]2 years ago
6 0

If you mean f(x)=x+\frac1x, then the derivative is

\displaystyle f'(x) = \lim_{h\to0} \frac{\left(x+h+\frac1{x+h}\right) - \left(x+\frac1x\right)}h \\\\ = \lim_{h\to0} \frac{(x+h)-x}h + \lim_{h\to0} \frac{\frac1{x+h} - \frac1x}h \\\\ = \lim_{h\to0} \frac hh + \lim_{h\to0} \frac{x-(x+h)}{hx(x+h)} \\\\ = \lim_{h\to0} 1 - \lim_{h\to0} \frac h{hx(x+h)} \\\\ = 1 - \lim_{h\to0} \frac1{x(x+h)} \\\\ = \boxed{1 - \frac1{x^2}}

If you mean f(x) = \frac{x+1}x = 1 + \frac1x, we know from above that

\displaystyle \left(\frac1x\right)' = \lim_{h\to0} \frac{\frac1{x+h}-\frac1x}h = -\frac1{x^2}

which leaves the constant term, whose derivative is

\displaystyle (1)' = \lim_{h\to0}\frac{1 - 1}h = 0

and so

f'(x) = -\dfrac1{x^2}

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After reading your question I have come up with the correct way to factor (x-4) and (x-3) together:

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Answer:

t\approx 5.865\,s

Step-by-step explanation:

The motion equations that describe the ball are, respectively:

x = \left[\left(152\,\frac{ft}{s} \right)\cdot \cos 52^{\circ} \right] \cdot t

y = 4.5\,ft + \left[\left(152\,\frac{ft}{s} \right)\cdot \sin 52^{\circ} \right] \cdot t - \frac{1}{2}\cdot \left(32.174\,\frac{ft}{s^{2}} \right) \cdot t^{2}

The time required for the ball to hit the ground is computed from the second equation. That is to say:

4.5\,ft + \left[\left(152\,\frac{ft}{s} \right)\cdot \sin 52^{\circ} \right] \cdot t - \frac{1}{2}\cdot \left(32.174\,\frac{m}{s^{2}} \right) \cdot t^{2} = 0

Given that formula is a second-order polynomial, the roots of the equation are described below:

t_{1}\approx 5.865\,s and t_{2} \approx -0.048\,s

Just the first root offers a realistic solution. Then, t\approx 5.865\,s.

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tim brought a car 25000 and it depreciation $350 per year. What is the value of the car after 6 years?
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Answer:

22900

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Note that there are two scale models with each of ratio of 1/2 and 1/16 respectively.

For the first model, the dimension will be as follows:

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For the second model, the dimension will be as follows:

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The dimensions of the second model is 94/16 by 50/16 = 5.875 feet by 3.125 feet.

Since we are to solve for the area of the smallest scale model which is

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