find the first principle f(x)=1/x

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Assuming you require the derivative of f(x) from first principles, then

f' (x) = \(lim_{h>0}\) \(\frac{f(x+h)-f(x)}{h}\)

       = \(lim_{h>0}\) \(\frac{\frac{1}{(x+h)}-\frac{1}{x} }{h}\)

       = \(lim_{h>0}\) \(\frac{\frac{x-(x+h)}{x(x+h)} }{h}\)

       = \(lim_{h>0}\) \(\frac{\frac{x-x-h}{x(x+h)} }{h}\)

        = \(lim_{h>0}\) \(\frac{-h}{hx(x+h)}\) ← cancel h on numerator/ denominator

        =  - \(\frac{1}{x^2}\)


Related Questions

Which of the following numbers is an integer?

Question 2 options:

-3.293

-2.5

5/8

12/2

Answers

Answer:

12/2

Step-by-step explanation:

An integer is a whole number. All of the other possible answers are decimals and simplified fractions. 12/2 is a fraction, but can be simplified to a whole number, 6. 6 is an integer.

40% of what number is 60

Answers

Answer:

24

Step-by-step explanation:

Lets make this simple, divide it by 10 then mulitiply by 4 and there you go

Answer:

150

Step-by-step explanation:

Assume: (1) FIT calculated by percentage method; (2) Social Security 6.2% on $128,400; and Medicare 1.45%.Cumulative balance before this payroll is below maximum as related to cumulative earnings in calculating Social Security. (Round your answers to the nearest cent.)

Answers

The missing quantities are

Social Security= $217

Medicare = $‭50.75‬

Net Pay is $‭2,633.67‬

First, Taxable income is therefore;

= 3,500 - (76.90 x 4 )

= $‭3,192.4‬0

Federal Income Tax (FIT).

With taxable income of $‭3,192.4‬0, the tax is $565.15 plus 28% of anything above $‭3,073.

= 565.15 + (28% x (‭3,192.4‬0 - 3,073))

= 565.15 + 33.43

= $‭598.58

and, Social Security

= Gross pay x 6.2%

= 3,500 x 6.2%

= $‭217‬

and, Medicare

= 3,500 x 1.45%

= $‭50.75‬

Then, the Net Pay

= 3,500 - 598.58 - 217 - 50.75

= $‭2,633.67‬

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.......... do it now? Can't I do it later?

a) I've to
b) Have I
c) Do I have to
d) Should I

Answers

Answer:

d

Step-by-step explanation:

You are asking a question trying to suggest whether it can be done later

Mr. Smith and Mr. Stein were driving to a business meeting 140 miles from their office. Mr. Smith drove the first
miles, then Mr. Stein drove the rest of the way.

Write an algebraic expression for how many miles Mr. Stein drove.

Answers

The distance that Mr. Stein drove can be represented by the expression: \(140 - x\)

What is an algebraic expression?

A mathematical phrase made up of one or more variables, constants, and arithmetic operations like addition, subtraction, multiplication, and division is known as an algebraic expression. Exponentiation and other mathematical operators could also be present.

Let's assume that Mr. Smith drove "x" miles before Mr. Stein took over the driving.

Then, the total distance they traveled is 140 miles.

So, the distance that Mr. Stein drove can be represented by the expression:

140 - x

Therefore, This is because if Mr. Smith drove "x" miles, then the remaining distance that needed to be covered by Mr. Stein would be the difference between the total distance of 140 miles and the distance already driven by Mr. Smith.

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Find the value of y.

Find the value of y.

Answers

The value of y is 4√3

What are similar triangles?

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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When a coin is tossed it is either heads or tails. Suppose heads has a point value of 1 and tails a point value of -1. if the sum of the point value after 50 tosses is 14. How many of the tosses must have been heads?

Answers

Answer:

32

Step-by-step explanation:

Totally there are 50 tosses.  

Let the number of tosses which resulted head be x.  

Therefore the number of tosses which resulted tail is 50−x.

We get x×1+(50−x)×(−1)=14

x−(50−x)=14

x−50+x=14

x=32

please help a brother out

please help a brother out

Answers

Answer:

Plot points (4, -1), (1, -3), (1, -4), and (4, -4)

Step-by-step explanation:

All you had to do was change the negative signs to a positive sign.

Find the inverse function in slope-intercept form (mx+b):
f(3) = 5x – 15

Answers

Answer:

m=5

Step-by-step explanation:

Sam is practicing speed skating at an ice rink.The distance around the rink is 150 yards. He skated around the rink 5 times. How many feet did Sam skate

Answers

2250 feet
u multiply 150*5 and then convert 750 yards to feet
I believe 2250 feet because 150 yards is 450 in feet times 5 is 2250. hope this helps!

Write the expanded form of the expression. − 1/8(y+x)

Answers

Answer:

(-1/8 * y) + (-1/8 * x)

Answer:

Solution:

the expanded form of the expression. − 1/8(y+x)

=-y/8 +-x/8

a student finished 8 of her homework problems in class if the ratio problem she finished her problem she has left with 4:1 how many homework problems did she have total ​

Answers

Step-by-step explanation:

b HD hks Gojng umd book is Rio hz Wii

Duane begins paying a $5,000
student loan with an annual interest rate of 6.5%
compounded monthly. He schedules monthly payments of $118.57
for 4
years.

The following table shows the first payment in the amortization schedule.


Payment
Number Loan
Amount Payment Interest Principal Remaining
Balance
1
$5,000.00
$118.57
?

What amount of Duane's first payment goes to interest?
Responses

Answers

The amount of Duane's first payment that goes to interest is approximately $26.47.

To determine the amount of Duane's first payment that goes to interest, we need to use the amortization formula for a loan.

The formula to calculate the interest portion of a loan payment is:

Interest = Remaining Balance * Monthly Interest Rate.

Let's calculate the interest for the first payment using the given information:

Loan Amount = $5,000.00

Monthly Payment = $118.57

First, we need to calculate the monthly interest rate:

Monthly Interest Rate = Annual Interest Rate / 12

= 6.5% / 12

= 0.00542

Next, we need to calculate the remaining balance after the first payment:

Remaining Balance = Loan Amount - Principal Paid

= $5,000.00 - $118.57

= $4,881.43

Finally, we can calculate the interest portion of the first payment:

Interest = Remaining Balance * Monthly Interest Rate

= $4,881.43 * 0.00542

= $26.47

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sin( 3pi/4 ) =
O A. 1/2
OB. -√2/2
O C. √3/2
O D. √2/2

Answers

Answer:

D

Step-by-step explanation:

sin  (  3pi / 4 )

 =  sin   (   pi   -   pi  /  4   )

 =  sin   (   pi / 4  )

 = 1/root(2)

  =  root(2) / 2

we have 30 pairs of scissors. 60% are right handed and 30% are left handed and the remaining pairs belong to Ms. Taylor. how many pairs of scissors belong to Ms. Taylor?​

Answers

2 gyyuiiiuhhhhvvv. Gggg

Identify whether or not the relation is a function a yes b no
And how does it change

Identify whether or not the relation is a function a yes b no And how does it change

Answers

Answer:

Not a function

Step-by-step explanation:

This is not a function. It will fail the vertical line test.  For any value of x, there are two different y values.  This tells us that it is not a function

A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean μ = 1000, find the probability that both of the lamp's bulbs fail within 1000 hours.

Answers

Answer:

(e-1-1)2=0.3996

Step-by-step explanation:

Equations from Graphs
Which is the equation of the given line in point-
Please help me

Equations from GraphsWhich is the equation of the given line in point- Please help me

Answers

Answer:

A. y = -x + 8

Step-by-step explanation:

y = mx + c

m = \(\frac{y2 - y1}{x2 - x1}\) = \(\frac{0 - 8}{8 - 0}\) = -1

c = 8

=> The equation will be y = -1x + 8 or y = -x + 8.

What fraction is equal to 30%

Answers

Answer:

30/100 or 3/10

Step-by-step explanation:

A percent is out of 100. So since 30 is an even number then it would be 30/100 or 3/10.

fresh strawberries usually cost $2.25 at the local grocery store . This week they are discounted 10%? What is the price per pound, for strawberries ,this week. round the to two decimals

Answers

Answer:

$2.03

Step-by-step explanation:

2.25-(2.25*.1)=2.025

Discount:-

\(\\ \tt\longmapsto 0.1(2.25)\)

\(\\ \tt\longmapsto 0.22\)

Price after deducting discount

\(\\ \tt\longmapsto 2.25-0.22\)

\(\\ \tt\longmapsto \$2.03\)

Done

Determine if the three given side
lengths form a right triangle.
10 cm, 15 cm, 20 cm

Answers

Answer:

It doesn't form a right triangle

Step-by-step explanation:

According to the Pythagorean theorem, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

a^2 + b^2 = c^2 by substituting the three values, 10, 15, and 20 you should get an equivalent value of the hypotenuse.

10^2 + 15^2 = 20^2

100 + 225 = 400

325 =/= 400

This is false.

Since this is not equivalent, it is NOT a right triangle.

Hope this helped :)

One of the lamp posts at a shopping center has a motion detector on it, and the equation (x+16)2 + (y-13)² = 36 describes the boundary within which motion can be sensed. What is the greatest distance, in feet, a person could be from the lamp and be detected? A. 6 ft B. 12 ft C. 36 ft D. 72 ft​

Answers

The greatest distance, in feet, a person could be from the lamp and be detected is: B. 12 ft

How to find the  greatest distance?

The equation (x+16)² + (y-13)² = 36 describes a circle with center (-16,13) and radius 6. The motion detector on the lamp post can detect motion within this circle.

To find the greatest distance a person could be from the lamp and still be detected, we need to find the diameter of the circle, which is equal to twice the radius. Therefore, the greatest distance a person could be from the lamp and still be detected is 2(6) = 12 feet.

Therefore, the correct answer is B) 12 ft.

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Problem 5.A miner is trapped inside a mine and has access to 3 doors. The first door leads to a tunneland can take him to safety in 3 hours. The second door is a trap and brings him back to the mine againafter 5 hours through a tunnel. The third door also is a trap that brings him back to the mine after 7 hoursthrough a tunnel. The miner at all times is equally like to choose any of the doors. (In the darkness he canhardly distinguish the three). What is the expected length of time until he reaches safety

Answers

Answer:

Expected time is 15 hours for him to get to safety.

Step-by-step explanation:

We define X as the time that this miner would get to safety.

We define Y as the door he chooses initially.

P(Y= 1) = P(Y=2)=P(Y=3) = 1/3

We have E[X|Y=1] = 3

E[X|Y] = 5 hours + E[X}

E[X|Y] = 7 hours + E[X]

Then we have

E[X] = 1/3(3 + 5 + E[X] + 7 + E[X])

We cross multiply

3*E[X] = (15 + 2E[x])

3E[X] - 2E[X] = 15

E[X] = 15

So the time it would take to get him to safety is 15 hours

consider the following data for a dependent variable y and two independent variables, x1 and x2 . x 1 x 2 y 30 12 94 46 11 109 24 17 112 51 16 178 41 6 94 51 19 176 74 7 171 37 13 117 60 13 142 77 16 212 round your all answers to two decimal places. enter negative values as negative numbers, if necessary.

Answers

The correlation coefficient for x1 and y is 0.91, The correlation coefficient for x2 and y is 0.55 and The correlation coefficient for x1 and x2 is -0.33

Calculating the Correlation Coefficient for x1 and y:

Step 1: Calculate the mean of x1:  Mean of x1 = (30 + 46 + 24 + 51 + 41 + 51 + 74 + 37 + 60 + 77) / 10  Mean of x1 = 47.1

Step 2: Calculate the mean of y:  Mean of y = (94 + 109 + 112 + 178 + 94 + 176 + 171 + 117 + 142 + 212) / 10  Mean of y = 134.1

Step 3: Calculate the standard deviation of x1:  Standard Deviation of x1 = √(((30 - 47.1)2 + (46 - 47.1)2 + (24 - 47.1)2 + (51 - 47.1)2 + (41 - 47.1)2 + (51 - 47.1)2 + (74 - 47.1)2 + (37 - 47.1)2 + (60 - 47.1)2 + (77 - 47.1)2) / 10)

Standard Deviation of x1 = 17.43  

Step 4: Calculate the standard deviation of y:  Standard Deviation of y = √(((94 - 134.1)2 + (109 - 134.1)2 + (112 - 134.1)2 + (178 - 134.1)2 + (94 - 134.1)2 + (176 - 134.1)2 + (171 - 134.1)2 + (117 - 134.1)2 + (142 - 134.1)2 + (212 - 134.1)2) / 10)

Standard Deviation of y = 38.82  

Step 5: Calculate the covariance of x1 and y:  Covariance of x1 and y = ((30 - 47.1) × (94 - 134.1) + (46 - 47.1) × (109 - 134.1) + (24 - 47.1) × (112 - 134.1) + (51 - 47.1) × (178 - 134.1) + (41 - 47.1) × (94 - 134.1) + (51 - 47.1) × (176 - 134.1) + (74 - 47.1) × (171 - 134.1) + (37 - 47.1) × (117 - 134.1) + (60 - 47.1) × (142 - 134.1) + (77 - 47.1) × (212 - 134.1)) / 10  

Covariance of x1 and y = 393.3

Step 6: Calculate the correlation coefficient of x1 and y:

Correlation Coefficient of x1 and y = Covariance of x1 and y / (Standard Deviation of x1 × Standard Deviation of y)  = 393.3 / (17.43 × 38.82)

Correlation Coefficient of x1 and y = 0.91

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consider the following data for a dependent variable y and two independent variables, x1 and x2. x 1 x 2 y 30 12 94 46 11 109 24 17 112 51 16 178 41 6 94 51 19 176 74 7 171 37 13 117 60 13 142 77 16 212 round your all answers to two decimal places. enter negative values as negative numbers, if necessary. Show the correlation coefficient for each variable

Which expression is equivalent to 3\dfrac78 - 6\dfrac143 8 7 ​ −6 4 1 ​ 3, start fraction, 7, divided by, 8, end fraction, minus, 6, start fraction, 1, divided by, 4, end fraction?

Answers

Answer:

\(-2\dfrac{3}{8}\)

Step-by-step explanation:

Given the expression:

\(3\dfrac78 - 6\dfrac14\)

We are to simplify and obtain an equivalent expression.

Step 1: Change to Improper Fractions

\(3\dfrac78 - 6\dfrac14=\dfrac{31}{8}-\dfrac{25}{4}\)

Step 2: Take the Lowest Common multiple of the denominators

LCM of 8 and 4 is 8.

Therefore:

\(\dfrac{31}{8}-\dfrac{25}{4}=\dfrac{31-2(25)}{8}\\\\\dfrac{31-50)}{8}\\\\=-\dfrac{19}{8}\\\\=-2\dfrac{3}{8}\)

Therefore, an equivalent expression to \(3\dfrac78 - 6\dfrac14\) is \(-2\dfrac{3}{8}\).

Answer

3  7/8+ (-6  1/4)

Step-by-step explanation:

Ok Billy needs 90 lbs of garden soil to landscape a building. In the company storage area, he finds 2 cases holding 24 3/4 soil each, and a third case holding 19 3/8 lb. How much gardening does Bill still need in oder to do the job?

Answers

Answer:

1/3

Step-by-step explanation:

mrs.johnson is working on math with a group of students. she has a total of 15 students. 9 of them are girls. what is the ratio of boys to girls for mrs.johnsons math group?

make sure you simplify all ratios and fractions

Answers

Answer:

6

Step-by-step explanation:

the rest are boys

absolute value of 7 and one
eigth

Answers

The absolute value of 7 and 1/8 is 7 and 1/8! If you have to add these two values then it would be 7 1/8. Absolute value just means both values will be positive. Hope this helps!


Please give brainliest❤️

Need help with this- Precalculus

Need help with this- Precalculus

Answers

use x^2 when x=0 because the restriction for it is "use x if x is less than or equal to 1"

when x = 0, (0)^2 will make f(x) = 0

the graph of f(x) will just be a dot at 0

Find the value of x

Find the value of x

Answers

Answer:

x=12

(90-35)-7/4

Answer:

x=12

Step-by-step explanation:

Since the two angles are complementary, both angles add up to 90°.

So, to find the value of the other angle, simply subtract 35 from 90.

90-35=55

Now we know that the expression is equal to 55.

4x+7=55

Subtract 7 from both sides.

4x=48

Divide both sides by 4.

x = 12

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