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2 years ago

Use the four-step definition of the derivative to find f'(x) if f(x) = −4x^3 −1.

1 answer:

7 0

$\stackrel{de finition \textit{ of a derivative as a limit}}{\lim\limits_{h\to 0}~\cfrac{f(x+h)-f(x)}{h}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[-4(x+h)^3-1]~~ - ~~[-4x^3-1]}{h} \\\\\\ \cfrac{[-4(x^3+3x^2h+3xh^2+h^3)-1]~~ ~~+4x^3+1}{h} \\\\\\ \cfrac{[-4x^3-12x^2h-12xh^2-4h^3-1]~~ ~~+4x^3+1}{h} \\\\\\ \cfrac{-4x^3-12x^2h-12xh^2-4h^3-1+4x^3+1}{h}\implies \cfrac{-12x^2h-12xh^2-4h^3}{h}$

$\cfrac{h(-12x^2-12xh-4h^2)}{h}\implies -12x^2-12xh-4h^2 \\\\\\ \lim\limits_{h\to 0}~-12x^2-12xh-4h^2\implies \lim\limits_{h\to 0}~-12x^2-12x(0)-4(0)^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \lim\limits_{h\to 0}~-12x^2~\hfill$

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Question c please, it’s about probabilities. i attached photo

Reil [10]

Answer:

200

Step-by-step explanation:

Assuming all of the pie chart sections are equal.

There are 5 equal sections so divide the 1000 spins by 5 and you get 200

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3 years ago

Read 2 more answers

What is -1/19,7/4,-4/7 in least to greatest

r-ruslan [8.4K]

Answer:

-4/7 is the smallest. then it's -1/19 and then finally it's 7/4

7 0

2 years ago

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In Applied Life Data Analysis (Wiley, 1982), Wayne Nelson presents the breakdown time of an insulating fluid between electrodes

ale4655 [162]

Answer:

The sample mean is $\bar{x}=14.371$ min.

The sample standard deviation is $\sigma = 18.889$ min.

Step-by-step explanation:

We have the following data set:

$\begin{array}{cccccccc}0.15&0.82&0.81&1.44&2.70&3.28&4.00&4.70\\4.96&6.49&7.25&8.03&8.40&12.15&31.89&32.47\\33.79&36.80&72.92&&&&&\end{array}$

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values.

The formula for the mean of a sample is

$\bar{x} = \frac{{\sum}x}{n}$

where, $n$ is the number of values in the data set.

$\bar{x}=\frac{0.15+0.82+0.81+1.44+2.7+3.28+4+4.7+4.96+6.49+7.25+8.03+8.4+12.15+31.89+32.47+33.79+36.80+72.92}{19}\\\\\bar{x}=14.371$

The standard deviation measures how close the set of data is to the mean value of the data set. If data set have high standard deviation than the values are spread out very much. If data set have small standard deviation the data points are very close to the mean.

To find standard deviation we use the following formula

$\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} }$

The mean of a sample is $\bar{x}=14.371$ .

Create the below table.

Find the sum of numbers in the last column to get.

$\sum{\left(x_i - \overline{X}\right)^2} = 6422.0982$

$\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} } = \sqrt{ \frac{ 6422.0982 }{ 19 - 1} } \approx 18.889$

7 0

2 years ago

Solve this equation 53y - 55 = 42y

stiv31 [10]

53y-42y=55
11y=55
Y=55/11 =5

6 0

2 years ago

Read 2 more answers

b is the midpoint of AC and E is the midpoint of BD if A(-9,-4) C(-1,6) and E(-4,-3) find the coirdinates of D

natima [27]

To find the coordinate of the point D, we can use the Midpoint point of a line Segment formula. Calculation of the formula are as follows,

Given two points A(x1,y1) and C(x2,y2), we need to locate the midpoint coordinate of this line denoted as B(x,y).

To solve for the value of x and y, we get,

x=(x1+x2)/2 and y=(y1+y2)/2

For the given problem, we need to solve first the midpoint coordinate of AC which is B.

So, A(-9,-4)=A(x1,y1) and C(-1,6)=C(x2,y2)

Hence,

B(x,y)=B((-9+(-1))/2, (-4+6)/2)=B(-10/2,2/2)=B(-5,1)

Now, since the midpoint is given but one point in the line is missing. To solve for the missing point D(x2,y2), we need to use the Midpoint Segment Formula.

That is, B(-5,1)=B(x,y) and E(-4,-3)=E(x1,y1)

So,

x=(x1+x2)/2 and y=(y1+y2)/2

-5=(-4+x2)/2 and 1=(-3+y2)/2

By Cross Multiplication and Transposing method,

-5(2)=-4+x2 and 1(2)=-3+y2

x2=-10+4=-6 and y2=3+2=5

Thus, the coordinate of D is D(-6,5).

5 0

3 years ago