Evaluate the limit

[tex]\lim \limits_{x\to 0} \dfrac{\ln \left(1-\dfrac x4 \right) - (1-x)^{\tfrac 14} +1}{x^2}[/tex]

Answers

Answer 1

Answer:

1/16

Step-by-step explanation:

Place x=0 and you can see [tex]\frac{0}{0}[/tex] indefinitness. So you can apply the l'hosptial rule. Its basic you should

[tex]\lim_{x \to \ 0} \frac{g(x)}{f(x)} = \\[/tex]  [tex]lim_{x \to \ 0} \frac{g'(x)}{f'(x)}[/tex] so apply the derivative

[tex]\frac{\frac{1}{x-4} +\frac{1}{\sqrt[4]{(1-x})^3 } }{2x}[/tex] and replace the x=0 and you'll see same answer [tex]\frac{0}{0}[/tex] re-apply the l'hospital rule and answer

[tex]\frac{\frac{-1}{(x-4)^2} + \frac{3}{16\sqrt[4]{(1-x)^7} } }{2}[/tex] and replace the 0 you can see the answer [tex]\frac{1}{16}[/tex]


Related Questions

which list of fraction is in order from least to greatest value

Answers

You can divide the fractions to make them decimals & then that will make it easier to list them

Solve for x
Can you pls help me?

Answers

Answer:

6x+50=92

Step-by-step explanation:

The x is for how much the classes cost plus the amount they charged her for the gear.

The following equation models the deer population during mating season starting April 1, 2016, where m is time in months.

1053(1.23)^m = N

(a) How many deer were there on April 1, 2016?

(b) How many deer were there on May 1, 2016?

(c) What is the monthly growth rate?

(d) What is the yearly growth rate?

(e) What is the weekly growth rate?

Answers

The function N =1053(1.23)^m or 1053(1.23)^m = N is an illustration of an exponential function

The deer on April 1, 2016

The function is given as:

N =1053(1.23)^m

On April 1, 2016; the value of m is:

m = 0

So, we have:

N =1053(1.23)^0

N = 1053

Hence, there are 1053 deers on April 1, 2016

The deer on May 1, 2016

The function is given as:

N =1053(1.23)^m

On April 1, 2016; the value of m is:

m = 1

So, we have:

N =1053(1.23)^1

N =1295

Hence, there are 1295 deers on May 1, 2016

The monthly growth rate

An exponential growth function is represented as:

y = a(1 + r)^x

Where r represents the growth rate

By comparison; the monthly growth rate (r) is calculated as:

1 + r = 1.23

Subtract 1 from both sides

r = 0.23

Express as percentage

r = 23%

Hence, the monthly growth rate is 23%

The yearly growth rate

We have the monthly growth rate to be 23%

There are 12 months in a year.

So, the yearly growth rate is:

y = 23%^12

Evaluate

y = 0.00022%

Hence, the yearly growth rate is 0.00022%

The weekly growth rate

We have the monthly growth rate to be 23%

There are 4 weeks in a months

So, the weekly growth rate is:

m = 23%^(1/4)

Evaluate

m = 69%

Hence, the weekly growth rate is 69%

Read more about exponential functions at:

https://brainly.com/question/11464095

Students from four classes are in talent show. A. There are 28 students in Ms. Fiona's class. The ratio of her student who are in the talent show to those who are not in the talent show is 2:5. How many of Ms. Fiona's students are in the talent show? B. Mr. Juan has 24 students in his class. Some of his students are also in the talent show. Explain why it is not possible for exactly 24% of the students in Mr. Juan's class to be in the talent show. C. The rest of the students in the talent show are from Mrs. Lee's class and Mr. Greg's class. • Mrs. Lee has 23 students in her class, and 7 of them are in the talent show. There are 4 more students from Mr. Greg's class than from Mr. Juan's class in the talent show. The number of students in the talent show from Mrs. Lee's class is greater than the number from Mr. Juan's class and fewer than the number from Mr. Greg's class. In all, 30% of the students in these three classes are in the talent show, Show or explain why there must be exactly 23 students in Mr. Greg's class. As part of the explanation, determine how many students from Mr. Greg's class are in the talent show​

Answers

Answer:

B

Step-by-step explanation:

i had this question on my test

The difference is
Part B 287
Find the product of the expressions.

Answers

Answer:

12

Step-by-step explanation:

Solve by completing the square

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 8x = 33 [/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 8x +16 = 33 + 16 [/tex]

[tex]\qquad \sf  \dashrightarrow \: (x + 4) {}^{2} = 49[/tex]

[tex]\qquad \sf  \dashrightarrow \: x + 4 = \sqrt{49} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x + 4 = \pm7[/tex]

Hence, there are two solutions ~

1. when x + 4 = 7

[tex]\qquad \sf  \dashrightarrow \: x + 4 = 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 7 - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 3[/tex]

2. when x + 4 = -7

[tex]\qquad \sf  \dashrightarrow \: x + 4 = - 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = - 7 - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = - 11[/tex]

I hope you understood ~

A city that has an elevation of 15 meters is closer to sea level than a city that has an elevation of -10 meters.

Answers

Answer:

Step-by-step explanation: Your answer will be -10 because even though -10 is much lower than 15 it’s still closer to sea level.

Evaluate the expression (3-2i)(3-2i) and write the result in the form a+bi ,where a is the real part of your answer and bis the coefficient in front of the imaginary part

Answers

Answer:

a = 5, b = -12

Step-by-step explanation:

By basic factoring, you get 9 - 12i + [tex]4i^2[/tex]. Since [tex]i^2[/tex] is simply -1, the expression evaluates to 9 - 12i - 4, which is 5 - 12i.

eometry Part 4 - Lesson 1 Assessment - EDCP.MA004.D
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2 3 4 5
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What is the area of a sector of a circle with a central angle of measure 180° and whose radius is 5
cm? Leave your answer in terms of I.

o
ле?
o com
35
O 2 cm

Answers

Answer: it would be 34

Step-by-step explanation:

What would you do if fear was not a factor and you could not fail?`

i know it's not a maths question but let's try

Answers

Answer:

Well, i would just say you just had to do your best in everything that you do. No pressure , no stress don't overwork yourself and simply take action. Then you will have a chance to get what you want because you tried your best to get to it. Although sometimes we don't get what we want, atleast we'll be closer. As they say, 'Aim for the sun to reach the moon"

Step-by-step explanation:

You're welcome

how many cubic inches of hot air would be needed to completely inflate a 12 in diameter beach ball

Answers

Answer:

904.78 cubic inches

Step-by-step explanation:

Since a beach ball is a sphere, use the formula for volume, V = 4/3 * pi * r^3 to find the volume of the beach ball, using 6 for radius since diameter is two times the radius and the diameter is 12 inches. 4/3 * pi * 6^3 = 904.78, so that many cubic inches of air would be needed to inflate the beach ball.

Hopefully this helps- let me know if you have any questions!

250 gram as a percentage of 1 kg ​

Answers

Hey there!

Answer: 25%

[tex] \rightarrow \: (\sf{ \frac{250}{1000} ) \times 100}[/tex]

[tex] \rightarrow \: ( \sf{0.25) \times 100}[/tex]

[tex] \rightarrow \: \sf{ = 25\%}[/tex]

Answer:

25%

Step-by-step explanation:

the quantities must have the same units

1 Kg = 1000 grams

express the quantities as a fraction and multiply by 100%

[tex]\frac{250}{1000}[/tex] × 100% = 0.25 × 100% = 25%

Find a solution to the linear equation 13x+y=26 by filling in the boxes with a valid value of x and y.

Answers

Answer:

y = -13x+26

Step-by-step explanation:

13x+y=26

y= -13x+26


Rewrite the expression x -3/11
in radical form.

Answers

Hey i put the answer in the picture

Answer:

11x-3

11

Step-by-step explanation:

and that's the answer

If tanθ= 2 find cotθ using identities. This is in quad. 1.

Answers

Answer: 1/2

Step-by-step explanation:

Find the volume. Please help! Thanks!
hehe

Answers

Volume of a Square Pyramid: 1/3 x length x width x height

Length = 2

Width = 2

Height = 3

Volume = 1/3 x 2 x 2 x 3

Volume = 1/3 x 4 x 3

Volume = 1/3 x 12

Volume = 4

Volume = 4 cm^3

Hope this helps!

Margo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.



The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.



The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.



The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.



The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.



The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.



The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.



The total amount of wood Margo needs to build her pencil caddy is
square inchesv

Answers

Yes totally it’s fine bc what ammi t you will give and she creates it f51 wnat s it is not

Sandy brought 6 1/4 dozen cookies to the bake sale. Alejandro brought 1 3/4 fewer cookies than Sandy brought. Pierre brought 2 3/4 dozen fewer cookies than Alejandro brought. How many dozen cookies did Pierre bring? ​

Answers

Answer: 4 1/2 doezen cookies

Step-by-step explanation: just subtract. Hope this helps.

A radioactive substance decays exponentially. A scientist begins with 190 milligrams of a radioactive substance. After 19 hours, 95 mg of the substance remains. How many milligrams will remain after 36 hours?

Answers

Answer:

  51 milligrams

Step-by-step explanation:

Exponential growth or decay can be modeled by the equation ...

  y = a·b^(x/c)

where 'a' is the initial value, 'b' is the "growth factor", and 'c' is the time period over which that growth factor applies. The time period units for 'c' and x need to be the same.

In this problem, we're told the initial value is a = 190 mg, and the value decays to 95 mg in 19 hours. This tells us the "growth factor" is ...

  b = 95/190 = 1/2

  c = 19 hours

Then, for x in hours the remaining amount can be modeled by ...

  y = 190·(1/2)^(x/19)

__

After 36 hours, we have x=36, so the remaining amount is ...

  y = 190·(1/2)^(36/19) ≈ 51.095 . . . . milligrams

About 51 mg will remain after 36 hours.

A bag of fruit contains 3 apples, 2 oranges, 1 banana, and 4 pears, Gerald will randomly select two pieces of fruit
one at a time from the bag and not put them back. What is the probability that the first piece of fruit Gerald selects will be a banana and the second piece of fruit will be a pear?

Answers

Answer:

2/45

Step-by-step explanation:

The probability that a banana is picked for the first one is:

1/10

because there are 10 fruits and one of them is a banana,

Then, the second piece has to be a pear.

For this we have already picked one fruit out of the bag, which leaves 9 fruits in the bag.

There are 4 pears so the probability of picking a pear second is

4/9

To find the probability of a banana and then a pear, you want to multiply these values together

So:

1/10 x 4/9 = 4/90 = 2/45

So the probability is 2/45

What is the value of x? Enter your answer in the box.

Answers

Answer:

x = 8

y = 6

Step-by-step explanation:

First and foremost, it's an equilateral triangle, therefore all sides and angles are equal.

Knowing that the sum of angle in a triangle is 180°, therefore each angle is 60°.

Then equating (7x+4)° to 60, we have that,

7x+4=60

7x=60-4

7x=56

x=56÷7

x=8.

4 2 5 0
3 2 8 7
2 1 8 ?​

Answers

Answer:

5

Step-by-step explanation:

A team sells their jerseys for 40% more than it costs to have them made. What is the selling price of a jersey that cost the team $25.

Answers

Answer:

$35.

Step-by-step explanation:

SP = 25 + 0.40*25

= 25 + 10

= $35.

A consistent and dependent system is formed by the equations y = 3x + 9 and
6x – 2y = A, where A is a real number. Find the value of A.
-

Answers

Answer:

A = -18.

Step-by-step explanation:

We are given that y = 3x +9.

From this, we gather 3x - y = -9.

We then multiply both sides by 2 to get 6x – 2y = -18. Therefore, A = -18.

molly makes 70% of her free throws. The random numbers below represent 20 trials of a simulator of two free throws, using the numbers 9 through 0
38 38 21 50 64
71 66 42 47 90
80 82 29 98 27
87 89 89 93 03
let the numbers from --- to ----- represent a successful free throw.
let the numbers from ---- to ----- represent a missed free throw.
based on the simulated results, the probability that molly makes both free throws is
----- or ------%

Answers

The random number simulator of Molly's throws is an illustration of probability.

The probability of making both free throws is 30%

How to determine the probability?

From the complete question, we understand that:

The simulator is based on numbers 0 to 9

Given that she makes 70% of her free throws, then it means that 7 of the 10 numbers would represent a successful throw, while the other three would represent a missed throw

So, we have:

Let the numbers from 0 to 6 represent a successful free throw.Let the numbers from 7 to 9 represent a missed free throw.

From the random numbers, she has two successful free throws in:

21 50 64 66 42 03 --- 6 numbers of 20

The probability of making two free throws is then calculated as:

P = 6/20

Evaluate

P = 30%

Hence, the probability of making both free throws is 30%

Read more about probability at:

https://brainly.com/question/251701

Joy's class voted on whether or not to do science fair projects in groups. Out of 24 votes, 18
were in favor of working in groups. What percentage of the votes were in favor of working in
groups
Write your answer using a percent sign (%).
Submit

Answers

Answer:

75%.

Step-by-step explanation:

That would be (18/24) * 100

= 3/4 * 100

= 75%

The correct answer would be 75 percent

Write a qbasic progrsm to check pass or fail​

Answers

Step-by-step explanation:

CLS

INPUT " Enter total marks "; M

IF M > 40 THEN

PRINT "You are passed "

ELSE

PRINT " You are failed "

END IF

END..

I well give u brainliest
What are the x- and y-intercepts for the linear equation 2x – 4y = 8 ?

Question 6 options:

(4,0) and (0,-2)


(2,0) and (0,4)


(-2,0) and (4,0)


(-2,0) and (0,4)

Answers

The answer is a. (4,0) and (0,-2)

Find the volume of the prism.

Answers

Answer:

240 cm³

Step-by-step explanation:

Volume of prism= base area ×height

The base is a rectangle here, and its area has the formula of length ×breadth.

Given

length of base= 10 cm

breadth of base= 6 cm

height of prism= 4 cm

Base area

= 10(6)

= 60 cm²

Volume of prism

= 60(4)

= 240 cm³

Answer:

240 cm³

Step-by-step explanation:

Volume of a rectangular prism: l*w*h

L (length) : 10 cmW (width): 6 cmH (height): 4 cm

V = l*w*h  <== substitute the numbers (above) for the variables

V = 10*6*4

V = 60*4

V = 240 cm³ (cubed)

Hope this helps!

Make an accurate drawing of two rectangles with the same perimeter, but different areas. Indicate the dimensions of the rectangles, as well as the perimeter and the area in each figure.​

Answers

I don’t know what the answer is
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