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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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Answer:

49.8 ft²

Step-by-step explanation:

the picture in the attached figure

given:

a=3,  b=1   c=1.8

To know the surface area:

surface area of the figure=surface area of cube+surface area of triangular prism

first lets find out the area of cube and triangular prism.

surface area of cube=4*a²

surface area of cube= 4*3² => 36  ft²

surface area of triangular prism=2*[a*c]+2*[a*b/2]  = 2*[3*1.8]+[3*1]

surface area of triangular prism=10.8 +3  = >  13.8 ft²

Therefore,  surface area of the figure=36 ft²+13.8  ft²

surface area of the figure= 49.8 ft²

the answer is:

49.8 ft²

3 0
3 years ago
Evaluate the expression. Write your answer in scientific notation.
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5 0
2 years ago
What is the mean of the following data set?
worty [1.4K]

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B

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After adding them all together, we end up with 351. There are 12 numbers, so we do 351/12, getting 29.25.

6 0
2 years ago
During the dry month of August, one U.S. city has measurable rain on average only 4 days per month. Assume all months have 30 da
Doss [256]

Answer:

The average number of days that will pass between measurable rain is 7.5.

Step-by-step explanation:

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In which

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e = 2.71828 is the Euler number

\mu is the mean in the given time interval.

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\frac{1}{\frac{4}{30}} = \frac{30}{4} = 7.5

The average number of days that will pass between measurable rain is 7.5.

8 0
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