find the first principle derivative for 3/x with respect to x​

Answers

Answer 1

Given f(x) = 3/x, its derivative is

[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{f(x+h)-f(x)}h[/tex]

[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{\dfrac3{x+h}-\dfrac3x}h[/tex]

[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{\dfrac{3x-3(x+h)}{x(x+h)}}h[/tex]

[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{3x-3(x+h)}{hx(x+h)}[/tex]

[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{3x-3x-3h}{hx(x+h)}[/tex]

[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{-3h}{hx(x+h)}[/tex]

[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{-3}{x(x+h)} = \boxed{-\frac3{x^2}}[/tex]


Related Questions

Mr. Lynch bought some oranges and pears.
After giving away 10 oranges, he had twice
as many pears as oranges left. If he had 24
pears in the end, what was the ratio of
oranges to pears in the beginning?

Answers

Answer:

11: 12

Step-by-step explanation:

Let the number of oranges and pears Mr Lynch have initially be x and p respectively.

x -10= ½p

2(x -10)= p

p= 2x -20 -----(1)

Since Mr Lynch did not give any pears away, the number of pears at the end is the initial number of pears.

p= 24

Substitute p= 24 into (1):

2x -20= 24

2x= 24 +20 (+20 on both sides)

2x= 44

x= 44 ÷2

x= 22

[tex] \frac{x}{p} = \frac{22}{24} [/tex]

[tex] \frac{x}{p} = \frac{11}{12} [/tex]

Thus the ratio of orange to pears in the beginning is 11: 12.

Please anyone help me

Answers

Math Problem

If die is rolled two times, find the probably of getting "1'twice.

Math Answer

[tex] {1}\{36} [/tex]

Feel fre e too ask me

Please understand it

#BrainliestBunch

Which division is shown by the model?

Answers

Step-by-step explanation:

where the model step by step explanation

Can somebody help me Answer to this ??

Answers

X=7

c is the answer:

[tex]3x + 50 = 10x + 1 \\ 10x - 3x = 50 - 1 \\ 7x = 49 \\ x = \frac{49}{7} \\ x = 7[/tex]

X=7! Math always sucks

There are 5 seats in a bus. In how many different ways if there are 5 children. How many different ways are there if there are 4 children, and how many different ways are there if there are 3 children.

Answers

Answer:

5=1

4=5

i don't really know for the third one sorry but it's more than 11

Step-by-step explanation:

Se preguntó a 44 estudiantes por el tiempo, medido en minutos, que tardan en
llegar a su sitio de estudio. Las respuestas obtenidas fueron: 15,20,17,24,45,40,35,39,46,44,50,47,42,40,38,30,35,45,35,45,35,37,47,48,58,55,38,37,40,43,40,39,45,48,50,35,20,57,55,56,47,43,37,34,50,60
a) Clasifique la variable y construya la
TDF correspondiente al histograma.
b) Realice 4 interpretaciones de los
datos condensados en la TDF del punto a).
c) Realice el histograma, el polígono de
frecuencias y la ojiva de esta variable.

Answers

Answer:

sdfghjkl

Step-by-step explanation:

Hi there can someone please help me?
What is z and k when k+4z=42

Answers

Answer:

Solution given:

we have

k+4z=42

k=42-4z

and

k+4z=42

4z=42-k

dividing both side by 4

[tex]\frac{4z}{4}[/tex]=[tex]\frac{42-k}{4}[/tex]

z=[tex]\bold{\frac{42-k}{4}}[/tex]

find the length of side x to the nearest tenth

Answers

Answer:

x = 2 sqrt(3)/3

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 60 = 1 /x

x sin 60 =1

x = 1 /sin 60

x = 1 / sqrt(3)/2

x = 2 sqrt(3)/3

Which statement are true regarding the diagram?

Answers

Answer: 2,4 are definite answers i don't know abt the others- unfortunately..

Step-by-step explanation: Im in mid school..

Viết khai triển theo công thức nhị thức Niu-tơn (x + 1) ^ 5

Answers

Answer:

x^5+5x^4+10x³+10x²+5x+1

Step-by-step explanation:

Which is a pair of vertical angles?
∠VRU and ∠SRT
∠TRS and ∠VRW
∠TRV and ∠WRU
∠WRV and ∠SRW

Answers

Answer: ∠TRS and ∠VRW  (Choice B)

========================================================

Explanation:

Ignore ray RU. I would redraw the entire thing without ray RU as part of the picture. See below.

Notice how lines TW and SV intersect to form an X shape.

The angles TRS and VRW shown in red are opposite one another, so we consider them to be vertical angles. Vertical angles are always congruent.

Answer:

B ∠TRS and ∠VRW

Step-by-step explanation:

Find the slope of (3,-24)(19,-48)

Answers

Answer:

-3/2

Step-by-step explanation:

To find the slope, we use the slope formula

m = (y2-y1)/(x2-x1)

   = (-48- -24)/(19 -3)

   = (-48+24)/(19-3)

   = -24/16

   = -3/2

Answer:

[tex]-\frac{3}{2}[/tex]

Step-by-step explanation:

The slope of a line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:

[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let:

[tex](x_1, y_1)=(3, -24)\\(x_2, y_2)=(19, -48)[/tex]

Substitute into slope formula:

[tex]m=\frac{-48-(-24)}{19-3}=\frac{-24}{16}=\boxed{-\frac{3}{2}}[/tex]

The flow of water from a faucet can fill a
3-gallon container in 18 seconds. Give the ratio of gallons to seconds as a rate in gallons per second and as a reduced fraction.

Answers

Answer:

3/18 gallons/seconds, or 1/6 gallons/seconds

Step-by-step explanation:

We know that for every 3 gallons, the faucet fills that amount up in 18 seconds. Another way we can write that is "3 gallons for 18 seconds", or 3 gallons / 18 seconds.

Therefore, in terms of gallons to seconds, we can write this as 3 gallons/18 seconds.

One cool thing we can do with fractions is that if we multiply/divide the numerator by the same thing, the fraction is still the same amount, like if we divided by one. For example, if we multiply 1/10 by 10/10 = 1, we would get 10/100 = 1/10, changing the numbers but still keeping the fraction intact. We can apply this concept here to reduce the fraction.

Reducing the fraction means that we want to make the numerator and denominator as small as possible while still keeping them as integers. This means that, if possible, we should divide both the numerator and denominator by their greatest common factor (if it is greater than 1).

To find the greatest common factor, we can list factors and find the greatest one among them.

We have two numbers, 3 and 18.

The factors of 3 are 1 and 3 while the factors of 18 are 1, 2, 3, 6, 9, and 18. The greatest common number among these two is 3. Therefore, we can divide both these numbers by 3 to get

3/18 = 1/6 gallons/seconds as our answer

Find the value of x that makes m
n.
m
n
(180 - x)^

Answers

Answer:

x=180-x

2x=180

x=90

Step-by-step explanation:

Anyone know this question?

Answers

i think the answer is b

Literally what is this lol

Answers

Answer:

i think the first one- bc it should be 11x5pi but it would still end up as 55pi

Step-by-step explanation:

sorry if that doesnt help

2-5-9:0= 6797 so that’s yo answer

Problem 5

The sum of the first ten terms of an arithmetic progression consisting of positive integer terms is equal to the sum of the 20th, 21st and 22nd term. If the first term is less than 20, find how many terms are required to give a sum of 960.

Answers

Answer:

The answer is 15.

Step-by-step explanation:

Combine and simplify the following radical expression.

Answers

Answer:

[tex]24 \sqrt{5} [/tex]

Step-by-step explanation:

[tex]2 \sqrt{20} + 8 \sqrt{45} - \sqrt{80} [/tex]

[tex] = 2 \sqrt{2 \times 2 \times 5} + 8 \sqrt{3 \times 3 \times 5} - \sqrt{2 \times 2 \times 2 \times 2 \times 5} [/tex]

[tex] = 2(2 \sqrt{5} ) + 8(3 \sqrt{5} ) - (4 \sqrt{5} )[/tex]

[tex] = 4 \sqrt{5} + 24 \sqrt{5} - 4 \sqrt{5} [/tex]

[tex] = 24 \sqrt{5} (ans)[/tex]

Answer:

[tex]\huge\boxed{24\sqrt5}[/tex]

Step-by-step explanation:

[tex]2\sqrt{20}+8\sqrt{45}-\sqrt{80}\\\\=2\sqrt{4\cdot5}+8\sqrt{9\cdot5}-\sqrt{16\cdot5}\\\\\text{use}\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\=2\sqrt4\cdot\sqrt5+8\sqrt9\cdot\sqrt5-\sqrt{16}\cdot\sqrt5\\\\\text{we know}\ a\sqrt{b}=a\cdot\sqrt{b},\ \text{and}\ \sqrt{a}=b\iff b^2=a\\\\\text{Therefore}\\ 2\sqrt{4}=2\cdot\sqrt4=2\cdot2=4\\8\sqrt9=8\cdot\sqrt9=8\cdot3=24\\\sqrt{16}\cdot\sqrt5=4\cdot\sqrt5=4\sqrt5\\\\\text{Therefore}[/tex]

[tex]=2\sqrt4\cdot\sqrt5+8\sqrt9\cdot\sqrt5-\sqrt{16}\cdot\sqrt5=4\sqrt5+24\sqrt5-4\sqrt5\\\\=(4+24-4)\sqrt5=24\sqrt5[/tex]

A ball is dropped from a height of 9 feet and allowed to bounce. Each time the ball bounces, it reaches a height that is23the height of the previous bounce. How many times will the ball be exactly 3 feet above the ground? ​

Answers

I'm assuming you meant to say "it reaches a height that is 2/3 the height of the previous bounce".

We have a geometric sequence with a = 9 as the first term and r = 2/3 as the common ratio.

The nth term is a*(r)^(n-1) = 9*(2/3)^(n-1)

Set this equal to 3 and solve for n. You'll need logs to isolate the exponent.

9*(2/3)^(n-1) = 3

(2/3)^(n-1) = 3/9

(2/3)^(n-1) = 1/3

log[ (2/3)^(n-1) ] = log(1/3)

(n-1)*log(2/3) = log(1/3)

(n-1)*(-0.17609) = -0.47712

n-1 = (-0.47712)/(-0.17609)

n-1 = 2.7095235

n = 2.7095235+1

n = 3.7095235

Unfortunately we don't get a whole number. We can see that the terms of the sequence are:

9, 6, 4, 2.667

Each term is found by multiplying 2/3 by the previous term.

We don't land exactly on "3". The closest we get is 2.667 approximately.

So to answer the question, there is no way to get to exactly 3 feet above the ground based on a whole number of bounces.

solve for x. round to the nearest tenth of a degree, if necessary.​

Answers

x=30°

Answer:

Cos x°=adjacent/hypotenuse

Cos x°=45/52

x°=Cos-¹(45/52)

x°=30°

There is currently a linear bike path that goes through the points (4, 0) and (7, 4). The park commission is planning to build a new bike path that is parallel to the old one that passes through the point (2, 5).

Answers

Answer:

y = 3/4x +7/2

Step-by-step explanation:

slope of line = difference of 2nd x value - 1st x value/ 2nd y value - 1st y value

x difference /y difference = 3/4 = slope

y = 3/4x

to find y-intercept, add a variable

y = 3/4x + B

then add the first x and y value point numbers into equation

0 = 3/4(4) + B

-3 = B

put back B into equation.

y = 3/4x - 3 which is the linear path the biker is going

now you can use another variable to find the new bike path

y = 3/4x + A

plug in the x value 2 and y value 5 from (2,5)

5 = 3/2 + A

A = 7/2

there-fore the new line which is parallel to the old line is:

y = 3/4x +7/2

Identify the slope (m) and the y-intercept (b) of each line a) y= x+7 slope = y intercept = b) y = -3x slope = y intercept =

Answers

Answer:

a) y= x+7

The slope is 1 and the y intercept is 7

b) y = -3x

The slope is -3 and the y intercept is 0

Step-by-step explanation:

The slope intercept form of the equation of a line is

y = mx+b where m is the slope and b is the y intercept

a) y= x+7

The slope is 1 and the y intercept is 7

b) y = -3x

The slope is -3 and the y intercept is 0

Helpppppp plssssss ! Click the image

Answers

letter a since b, c, & d are all negative numbers

help me with this math question

Answers

Step-by-step explanation:

Option D

As time increases, the temprature of soup decreases..

hope it helps

Which of the following is an example of linear growth?
A. A baby gains 0.5% of its weight each week
B. An investment of $100 at an annual interest rate of 0.75%, compounded monthly
c. Depositing $5.00 in a savings account each week for t weeks
D. A bacterial culture doubles in size each day

Answers

Answer:

c. Depositing $5.00 in a savings account each week for t weeks

Step-by-step explanation:

Depositing $5.00 in a savings account each week for t weeks will be the correct example of linear growth.

What is a linear function?

A linear function is a function in which any two quantity varies linearly with respect to each other.

In another word, a linear function is that function whose slope will be constant and will plot a straight line.

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

The linear function will be that where the value of the next period can be calculated

For example y =2x here we can calculate y by just x

In given option (C) we can see that the difference between any two consecutive months can be calculated next month.

For more about the function

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The graphs below have the same shape. What is the equation of the blue
graph?

Answers

Answer:

C

Step-by-step explanation:

the answer is

[tex]{(x + 2)}^{2} [/tex]

Use braces and digits to indicate the set of whole numbers

Answers

Whole numbers are numbers without decimal points greater than or equal to 0.

The set of whole numbers is:

[tex]W =\{0,1,2,3,4.....\}[/tex]

In the introductory part of this solution, I stated that:

Whole numbers do not have decimal pointThe smallest whole number is 0

This means that the following numbers are whole numbers:

1, 9, 10, 67

While the following numbers are not:

-1, 9.0, 1.0, -67

Let W be the set of whole numbers; the set is:

[tex]W =\{0,1,2,3,4.....\}[/tex]

The dots after 4 means the set still continues

Read more at:

https://brainly.com/question/13106807

Answer:

The set of whole numbers W= {0,1,2,3,........,.....}

Step-by-step explanation:

The whole numbers are numbers that are complete. These numbers do not have a part missing or an additional part (fraction) for example decimals or fractions are not complete or whole numbers.

Braces are  curly brackets as shown { }

Digits are written inside the curly brackets to show the set of whole numbers.

The set of whole numbers is denoted by W.

W= {0,1,2,3,......,...}

The rational or irrational numbers which are expressed in decimals are not included in the list of whole numbers.

Here is a number machine input n --> -5 --> x4 --> _

Answers

Answer:

4(n - 5)

Step-by-step explanation:

The output is

n - 5 × 4 = 4(n - 5)

The output for the number machine will be 4 ( n - 5 ).

What is an expression?

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given the number, the machine is showing the expression written as:-

Output = 4 ( n - 5 )

For every value of n, there will be output.

Therefore, the output for the number machine will be 4 ( n - 5 ).

To know more about an expression follow

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One circle has a circumference of 12 pie Another circle has a circumference of 32 pie What is the ratio of the radius of the smaller circle to the radius of the larger circle?

Answers

Answer:

3 : 8

Step-by-step explanation:

The ratio of the radii is equal to the ratio of the circumference, then ratio is

12π : 32π ( divide both parts by 4π )

= 3 : 8

URGENT HELP PLZZZ I LOST MY BRAIN AND I'M OUT OF BATTERY

Write 5 irrational numbers between 2&3​

Answers

Answer:

Step-by-step explanation:

Irrational numbers are non terminating and non repeating numbers

Example: √2 , π

5 irrational numbers between 2&3​:

2.102003000.......

2.12345......

2.12030405.....

2.505006000....

2.606006000.....

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