Derivative this Problem.

Derivative This Problem.

Answers

Answer 1

[tex]\\ \sf\longmapsto {\displaystyle{\lim_{x\to 1}}}\dfrac{x^2-1}{x-1}[/tex]

[tex]\\ \sf\longmapsto {\displaystyle{\lim_{x\to 1}}}\dfrac{x^2-1^2}{x-1}[/tex]

[tex]\\ \sf\longmapsto 2(1)^(2-1)[/tex]

[tex]\\ \sf\longmapsto 2(1)[/tex]

[tex]\\ \sf\longmapsto 1[/tex]

Answer 2

Step-by-step explanation:

[tex] \tt \lim \limits_{x \to1} \frac{ {x}^{2} - 1 }{x - 1} = ...[/tex]

[tex] = \tt \lim \limits_{x \to1} \frac{(x + 1) \cancel{(x - 1)}}{ \cancel{(x - 1)}} [/tex]

[tex] = \tt \lim \limits_{x \to1}(x + 1)[/tex]

[tex] = \tt1 + 1[/tex]

[tex] = \boxed{ \bold{ \blue{ \underline2}}}[/tex]


Related Questions

Please take a look at the picture.

Answers

Answer:

A and B

Step-by-step explanation:

a) -x+0+(-x)=0

Combine like terms.

-2x+0=0

Subtract 0 from both sides.

-2x=0

Divide both sides by -2.

x=0

b) -x-(-x)=0

Remove parentheses.

-x+x=0

Combine like terms.

0=0

Hope this helps :)

City planners are planning to build a new community pool. They agree that the pool will be rectangular in shape, but the proposed dimensions changed. At the most recent meeting, it was determined that the width would remain at 11.6 meters but that the length would increase by 3.7 meters. So, the pool would now cover an area of 205.85 square meters.
Which equation can be used to determine the original length of the pool, l?


205.85=2(l+15.3)

205.85=11.6(l+3.7)

205.85=3.7(l+11.6)

Answers

The equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)

Let l be the original length of the pool.

Since the length of the pool is increased by 3.7 m, the new length L = l + 3.7.

Also, the area of the pool A = 205.85 square meter and it is a rectangle with width, W = 11.6 meters,

So, A = LW

Substituting the values of the variables into the equation, we have

A = LW

205.85 = (l + 3.7)11.6

So, the equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)

Learn more:

https://brainly.com/question/12932084

Answer:

Step-by-step explanation

205.85=11.6(l+3.7)

HIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

Answers

Answer:

The x-intercept is a point on the x-axis where the line crosses the x-axis and you can easily find it at point (-7, 0) because the line crosses the x-axis there.

Similarly, the y-intercept is a point on the y-axis where the line crosses the y-axis and you can easily find it at point (0, 2) because the line crosses the y-axis there.

Find the area of grass

Answers

Answer:

125m²

Step-by-step explanation:

find the area of ​​the green rectangle and remove the area of ​​the yellow rectangle

(12 - 2) * (16 - 2) - (6 * 2.5) =

10 * 14 - 15 =

140 - 15 = 125m²

A bag of sugar weighs 6²/⁵. What is the weight of 6¹/⁴ of such bag?
How many two thirds are there in 4¹/³?

Answers

Answer:

6 and a half 2 thirds are in 4 1/3

Step-by-step explanation:

2/3x=13/3

2x=13

x=6.5

it is predicted that by 2050 there will be 10^10 people living on earth. approximatrly will be 10^12 trees. how many trees for each person?


Answers

Interesting question. Does that mean near the end of humanity?

Solution 1:

10^10 = 1,000,000,000

10^12 = 100,000,000,000

100,000,000,000/1,000,000,000 = 100 trees per person

Solution 2:

10^12 / 10^10  ---  10^10 / 10^10

10^2/1 = 10^2 = 100 trees per person

Maximize z=200x+300y subject to x+2y<10 ,x+y<6,x>4 and x>0 ,y>0

Answers

Answer:

In theory I would have started looking at the critical points of the function, ie where the tangent plane is horizontal. Trick is, since the function is linear in both x and y the tangent plane is the curve itself, and it's never horizontal. We have to parametrize the border and look in there.

From the last two conditions ([tex]x>0; y>0[/tex]) we are looking only at the first quadrant. Let's start drawing lines.

The various restrains are color coded in the graph ([tex]x+2y<10[/tex] is red, [tex]x+y<6[/tex] is blue, [tex]x>4[/tex] is orange). That leads to the right triangle with a grey border that gets parametrized as shown. Due to the linearity of the original function, the maximum is at one of the extremes (upper or lower depending if the coefficient of the parameter is positive or negative). At this point is just calculating the values, pick up the largest, and see which points correspond to that value of the parameter.

Number crunching done, the maximum is at (4,2)

A certain star has a luminosity that is 5.9 times greater than that of our sun and a radius that is 2.8 times greater than the sun. What is the temperature of this star relative to the sun?

Answers

Answer:

16.5

Step-by-step explanation:

times the numberthen u will get your answer

0.7619047619 as a fraction?
which one
1. 1/16
2. 16/21
3. 2
4. 4

Answers

Answer:

16/21

Step-by-step explanation:


if line 1 has a slope of -4 and line 2 has a slope of 1/4, they are parallel
True
O False

Answers

Parallel lines need to have same slope
The lines have different slopes

It is false.

PLEASE HELP WITH THIS ONE QUESTION

Answers

Answer:

D. -3

Step-by-step explanation:

g(x) moved 3 units to the right

Determine if the given set of equations has 1 solution, no solution or infinitely many solutions. Include your reasoning for your answer.

y−2x=2
4y−8x=8

Answers

y-2x=2 has one solution
because it simplifies to y=2x+2 which is one solution

4y-8x=8 has one solution
because it simplifies to y=2x+2 which is one solution

hope this helps

Answer:

Infinitely many solutions

Step-by-step explanation:

Given system:

y - 2x = 24y - 8x = 8

Divide both sides of the second equation:

4y/4 - 8x/4 = 8/4y - 2x = 2

We got both equations same.

It means the lines representing the equations overlap, the system has infinitely many solutions.

ok. 4. 62 decreased by 2 7 co 8 anolo 5. 14 increased by 14​

Answers

Answer: Arachidonic acid (AA, sometimes ARA) is a polyunsaturated omega-6 fatty acid 20:4(ω-6), or 20:4(5,8,11,14).

Step-by-step explanation: It is structurally related to the saturated arachidic acid found in cupuaçu butter.[3] Its name derives from the New Latin word arachis (peanut), but it is important to note that peanut oil does not contain any arachidonic acid.[4]

Alguém me ajuda pfv rápido

Answers

Answer:

9.72

Step-by-step explanation:

1.8 x 1.8 x 3 = 9.72

Item 4 Evaluate. [(1 1/4−3/4)⋅(−2/3)3]÷(−4) What is the value of the expression? Enter your answer as a simplified fraction in the box.

Answers

Answer:

1/27

Step-by-step explanation: I took the quiz and the right answer is 1/27

The value of the given expression would be 0.25 which is simplified by using the PEMDAS rule in the expression.

What is PEMDAS rule?

The Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction rule is abbreviated as PEMDAS. This rule is used to answer the problem correctly and properly.

The given expression would be below as:

⇒ [(1 1/4−3/4)⋅(−2/3)3]÷(−4)

Using the PEMDAS rule in the above expression,

⇒ [(5/4−3/4)⋅(−2/3)3]÷(−4)

Apply the subtraction operation,

⇒ [(2/4)⋅(−6/3)]÷(−4)

Reduce the fractions, and we get

⇒ [(1/2)⋅(−2)]÷(−4)

Cancel out the terms of 2 to each other

⇒ (−1)÷(−4)

Cancel out the negative sign to each other

⇒ 1 / 4

Apply the division operation to get

⇒ 0.25

Therefore, the value of the given expression would be 0.25 which is evaluated.

To learn more about the Algebra link is given below.

brainly.com/question/953809

#SPJ5

Andre ran a 100 meter race in 12 seconds. What was his average speed as he ran?

Answers

his average speed as he ran: V = S/t = 100/12 = 25/3 (m/s)

ok done. Thank to me :>

Speed is the time rate at which an object is moving along a path. 25/3 is the average speed as he ran

What is Speed?

Speed is the time rate at which an object is moving along a path.

Speed =Distance/Time

His average speed as he ran:

V = S/t

Hundred by twelve.

= 100/12

Divide numerator and denominator by four.

Twenty five by three.

Average speed= 25/3 (m/s)

Hence if Andre ran a 100 meter race in 12 seconds. 25/3 is the average speed as he ran

To learn more on Speed click:

https://brainly.com/question/28224010

#SPJ5

Help help help help help help

Answers

Answer:

b

gnzjfzjgzjxjgzfjsngdjgsjfzgjskzjtztjsgjd5uduajai

The correct answer would be “D”

Which situation can be represented by this inequality 135 ≤ 10r + 15

Answers

[tex]135\leq 10r +15\\\\\implies 120 \leq 10r\\\\\implies 12 \leq r \\\\\implies r \geq 12 \\\\\text{Interval,}~~ [12,\infty)[/tex]

An elliptically shaped garden is surrounded by a wood walkway. The garden is 15 meters long and 8 meters wide. The walkway is 2.5 meters wide. Find the standard equation describing the ellipse formed by the walkway.

Answers

Answer:

x^2/b^2 + y^2/a^a = 1

Step-by-step explanation:

I believe that is the answer, also theanswerme answered this question. :)

Han earns $33.00 for babysitting 4 hours. At this rate, how much will he earn if he babysits for 1 hour?

Answers

Answer: $8.25

Step-by-step explanation: 33 divided by 4 (find unit rate)

Answer: $8.25

Step-by-step explanation:

Simply divide $33.00 by 4. 33/4 = 8.25

3^12*(2^x)^2 = 6^12 then x equals to..?​

Answers

Answer:

x=6

Step-by-step explanation:

Which one is the correct answer ? Find the amplitude , period. Phase shift asymptotes domain range Use the fact that cos(x)=0 will be an asymptote

Answers

Answer:

3. is your correct answer ok

Complete the table for the value of each digit in 123.

Answers

Answer:

1,2,3,4,5,6,7,8,9,10

2,4,6,8,10,12,14,16,18,20

3,6,9,12,15,18,21,24,27,30

Step-by-step explanation:

Can you help me with this ?:)

With explanation step-step Thanks

Answers

Part A

The given angle is 4pi/3. Multiply it by the factor 180/pi to convert from radians to degree mode.

Note how the given angle has pi in the numerator, while the conversion factor has pi in the denominator. The two pi terms will cancel.

(4pi/3)*(180/pi)

(4/3)*(180/1)

(4*180)/(3*1)

720/3

240

The angle 4pi/3 radians is equivalent to 240 degrees. This 240 degree angle is in quadrant 3. Any angle in this quadrant is between 180 degrees and 270 degrees, excluding both endpoints. This is the bottom left quadrant, aka the southwest quadrant.

Answer: Quadrant 3

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

Part B

To find the reference angle, we'll subtract off pi. This only works for angles in quadrant 3. This is because the first pi radians, aka 180 degrees, is taken up by the first two upper quadrants. The remaining bit in the third quadrant is all we care about to find the reference angle.

reference angle = (given angle in quadrant 3) - pi

reference angle = (4pi/3) - pi

reference angle = (4pi/3) - (3pi/3)

reference angle = (4pi - 3pi)/3

reference angle = pi/3

Answer: pi/3 radians

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

Part C

Use a calculator or a reference table to find that

tan(4pi/3) = tan(pi/3) = sqrt(3)

Alternatively, you can compute the sine and cosine values first

sin(pi/3) = sqrt(3)/2cos(pi/3) = 1/2

Dividing the two items in the order mentioned will get us the tangent value

tan = sin/cos

tan(pi/3) = sin(pi/3) divide cos(pi/3)

tan(pi/3) = sqrt(3)/2 divide 1/2

tan(pi/3) = sqrt(3)

In the jump from the second to last step, to the last step, the denominators '2' cancel out when dividing.

Answer:  sqrt(3)

Henry can run 2.5 miles in 1/4 of an hour if he maintains the same pace how many miles can Henry run in 1 1/2 hours

Answers

Answer:

Since Henry runs 2.5 miles every 15 minutes, he runs 5 miles in 30 minutes, 7.5 miles in 45 minutes, and 10 miles every 60 minutes.

explanation: just trust me

Answer:

60 minutes

Step-by-step explanation:

I hope this would help

Mr. Williams bought a plot of land for $ 40 000. The value of the land appreciated by 7% each year.

Answers

Answer:

no

Step-by-step explanation:


There are 10 circles and 2 triangles. What is the
simplest ratio of triangle to circle

Answers

5:1
5 being the circles, 1 being the triangles

Answer:

1:5

Step-by-step explanation:

put no. of triangles over no. circles because it asks triangles to circles

2/10

1/5........simplify

how do you solve 15 divided by 2/9

Answers

Answer:

67.5 or 67 1/2

Step-by-step explanation:

15   ÷              2

         ___________            

                   9

The numbers in 15 divided by 2/9 are labeled below:

15 = whole number

2 = numerator

9 = denominator

To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:

15 x 9 2  =     135

                       ____

                          2

Thus, the answer to 15 divided by 2/9 in fraction form is:

 135

_____

   2

To make the answer to 15 divided by 2/9 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:

135 / 2 = 67.5

The answer is rounded to the nearest two decimal points if necessary.

135/2 is an improper fraction and should be written as 67.5 or 67 1/2.

Hope this helps, have a nice day/night! :D

Answer:

67.5

Step-by-step explanation:

15 = 135/9

135/9 x 9/2 = 15 x 4.5 = 67.5

            9/2 = 4.5

Brainliest?

Please solve these algebraic questions? THANKS

Answers

Step-by-step explanation:

Note: I'm only providing solutions for Problem 9.

9. Simplify the following by collecting like terms:

Combining like terms involve performing the required mathematical operations (using the PEMDAS rule).  The terms must have the same degree (or exponents).  

 

a) 3a + 7a  

Add the coefficients of both terms.  

3a + 7a  = 10a

b) 4n + 3n

Add the coefficients of both terms.  

4n + 3n = 7n

c) 12y - 4y

Subtract the coefficient of both terms.  

12y - 4y = 8y

d) 5x + 2x + 4x

Add the coefficients of all terms.  

5x + 2x + 4x = 11x  

e) 6ab - 2ab - ba

The last term, "ba," can be rewritten as, "ab."  Remember that with algebraic expressions such as "ab," it essentially involves multiplication of both variables within the same term. Thus, ab = a × b. The variables ab also have a numerical coefficient of 1:  1a × 1b.

Now, we can perform the subtraction on all terms:

6ab - 2ab - ab = 3ab.  

f) 7mn + 2mn - 2mn

Subtract 2mn from 2mn, which leaves you with 7mn:

7mn + 2mn - 2mn = 7mn  

g) 4y - 3y + 8

For this algebraic expression, you could only combine the terms with the same variable and degree. Therefore, you'll have to subtract 3y from 4y, leaving the constant, 8, unaffected.  

4y - 3y + 8 = y + 8

 

h) 7x + 5 - 4x

Similar to question g, only combine the terms with the same degree and variable, leaving the constant unaffected.

7x + 5 - 4x = 3x + 5

i) 6xy + xy + 4y

You could only combine the terms with the same set of variables and degree, which are the first two terms on this given question. You cannot combine the last term, 4y, into the other terms.  

6xy + xy + 4y = 7xy + 4y

j) 5ab + 3 + 7ba

Using the same reasoning as in question e: the last term, 7ba, can be rewritten as 7ab, for which you could combine with the first term, 5ab.

5ab + 3 + 7ba = 12ab + 3  

k) 2 - 5m - m  

Combine the like terms, which are the second and the last term.  

2 - 5m - m = 2 - 6m

l) 4 - 2x + x

Combine the like terms, which are the second and the last term.  

4 - 2x + x = 4 - x  

1.02 = _____ hundredths

Answers

102 hundredths

102/100

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