find the limiting value using L hospital​

Find The Limiting Value Using L Hospital

Answers

Answer 1

Answer:

  -1

Step-by-step explanation:

The expression evaluates to the indeterminate form -∞/∞, so L'Hopital's rule is appropriately applied. We assume this is the common log.

  d(log(x))/dx = 1/(x·ln(10))

  d(log(cot(x)))/dx = 1/(cot(x)·ln(10)·(-csc²(x)) = -1/(sin(x)·cos(x)·ln(10))

Then the ratio of these derivatives is ...

  lim = -sin(x)cos(x)·ln(10)/(x·ln(10)) = -sin(x)cos(x)/x

__

At x=0, this has the indeterminate form 0/0, so L'Hopital's rule can be applied again.

  d(-sin(x)cos(x))/dx = -cos(2x)

  dx/dx = 1

so the limit is ...

  lim = -cos(2x)/1

  lim = -1 when evaluated at x=0.

_____

I find it useful to use a graphing calculator to give an estimate of the limit of an indeterminate form.

Find The Limiting Value Using L Hospital

Related Questions

2x-4>-14 or 2x-4\leq10

Answers

Answer:

x>0

Step-by-step explanation:

2x−4>−142x−4

Multiplica −14 y 2 para obtener −28.

2x−4>−28x−4

Agrega 28x a ambos lados.

2x−4+28x>−4

Combina 2x y 28x para obtener 30x.

30x−4>−4

Agrega 4 a ambos lados.

30x>−4+4

Suma −4 y 4 para obtener 0.

30x>0

El producto de dos números es >0 si ambos son >0 o <0. Puesto que 30>0, x debe ser >0.

x>0

solve the system of linear equations 3x-2y=16
6x-4y=32

Answers

Step by Step Solution

System of Linear Equations entered :

[1] 3x - 2y = 16

[2] 6x - 4y = 32

Solve by Substitution :

// Solve equation [2] for the variable x

[2] 6x = 4y + 32

[2] x = 2y/3 + 16/3

// Plug this in for variable x in equation [1]

[1] 3•(2y/3+16/3) - 2y = 16

[1] 0 = 0 => Infinitely many solutions

Infinitely many solutions

Answer:

Step-by-step explanation:

[1] 3x - 2y = 16

[2] 6x - 4y = 32

Solve equation [2] for the variable x

[2] 6x = 4y + 32

[2] x = 2y/3 + 16/3

Plug this in for variable x in equation [1]

[1] 3•(2y/3+16/3) - 2y = 16

[1] 0 = 0 => Infinitely many solutions

What is the y-coordinate of the solution of the system of equations?
Sy= 3x – 26
2x – y = 19
Enter your answer in the box.
y=

Answers

Answer: y=3x−262x−y=19

Step-by-step explanation:

Mr. Green is still repairing that old, rundown house he recently purchased. He finally fixed that leaky faucet in the kitchen, but now the bathroom faucet is leaking. He’s wondering if the dripping rate is the same as the kitchen, so again he starts his observations. However, this time he notes that for the bathroom faucet, 8 ounces of water dripped in 12 minutes.
A) At this rate, how many ounces of water will drip in a day?

Answers

Answer:

960 ounces in 1 day

(Sorry for a late response, I just logged on)

Step-by-step explanation:

Most of that information is negligable (not important) besides 8 ounces in 12 minutes.

so an hour is 60 minutes, if we multiply both parts of the problem by 5 we get

40 ounces in 1 hour

a day is 24 hours, so if we multiply both sides by 24 well get our answer

960 ounces a day

-- Gage Millar, Algebra 1/2 tutor

Answer:

960 ounces

Step-by-step explanation:

First, let's find how much water will drip in an hour (60 minutes), so we can make an equation:

8/12 = x/60

And if you multiply both sides of the equation by 60 you will get 8*5 = x which is 40. So, we know that in one hour, 40 ounces of water will drip from the bathroom faucet. To find how much water will drip in a day, just multiply 40 by 24 (since there are 24 hours in a day). That would result in 960.

Determine if this data is an example of a function
(3,-4);(3,-2);(3,0);(3,9)
Function or Relation

Answers

To be a function each x value creates a different y value.

The x value in the problem is the same for each set but the y values are all different so it is not a function.

Answer: relation

Split £10 into the ratio 4:1

Answers

Answer:

let the shares be 4x and 1x (4:1)

total share = 4x + 1x = 5x

total amount = 10£

5x = 10£

x = 2£

1st share = 4x = 4*2£ = 8£

2nd share = 1x = 1*2£ = 2£

.

.

[tex]{\bold{\red{HOPE\:IT\:HELPS!}}}[/tex]

[tex]\color{yellow}\boxed{\colorbox{black}{MARK\: BRAINLIEST!❤}}[/tex]

I have stopped going to school due to my mental break downs because of school so my teachers started sending me my work i have missed but the only thing i was not at school to learn how to do it so please help me....!!

Answers

Answer:

1. C.

2. A.

3. B.

i just know those im sorry-

Answer:

1 - c 6.4 ×10^6

2 - a 6.4 ×10

3- b 6.04 ×10^5

4) 5.21× 10^8 × 1.6km

=8.33×10^8 km

5) 10,000,000,000 = 1 ×10^10

BRAINLIST PLS

what is happening at this step in the equation solving process for 3x+7=5x
7=2x

Answers

Your subtracting 3x from 5x: 5x-3x
This is so you only have a variable on one side
3x+7=5x
-3x -3x
7=2x
(Divide both sides by 2)
x=3.5

What is the height, x, of the equilateral triangle?

Answers

Answer:

D: [tex]4\sqrt3[/tex]

Step-by-step explanation:

Draw the height. You notice you have split the triangle in two right triangles of sides 8 (the hypotenuse), 4 (half the horizontal side) and x. Let's apply Pythagorean theorem to the triangle: [tex]8^2 = 4^2+x^2 \rightarrow 64=16+x^2 \rightarrow x^2= 48 = 4^2\times3\\x= \sqrt48 = 4\sqrt3[/tex]

Kylie went into a grocery store and bought 5 apples and 4 bananas, costing a total of $10.50. Lily went into the same grocery store and bought 10 apples and 5 bananas, costing a total of $16.50. Determine the price of each apple (x) and the price of each banana (y). Remember, write it as money, with the whole and the decimal to the hundredths place!

Answers

Answer:

Apples $0.90 / Bananas $1.50

Step-by-step explanation:

So The equations would look like this

5x + 4y = 10.5

10x + 5y = 16.5

Solving for x, we get 2.1 - 4/5y

Substitute x

10(2.1 -4/5y) +5y = 16.5

Solving for y, we get 3/2 or 1.5

Substitute y

x = 2.1 -4/5(3/2)

x = 9/10

Now check the equations with the answers

5(9/10) + 4(3/2) = 10.5  ->  21/2 = 21/2

10(9/10) + 5(3/2) = 16.5  ->  33/2 = 33/2

Which means apples cost $0.90 and bananas cost $1.50

a shopkeeper sold an article at a gain of 5%.if he had sold it for rs. 16.50 less, he would have lost 5%.find the cost price of the article. ​

Answers

Answer:

m,ouih

-step explanation:

HELP PLZZ!!!!!
Find x.

Answers

Answer:

6.1

Step-by-step explanation:

So you would use tan as u are looking for the opposite and already have the adjacent.

tan(22) x 15 = 6.06 or 6.1

Answer:

x = 6.06

Step-by-step explanation:

tan (22°) = x/15

0.404 = x/15

x = 6.06

Please help me with this homework

Answers

Answer:

c

Step-by-step explanation:

S=B+1/2Pl

-b from both sides

s-b=1/2Pl

x2 to both sides

2(S-B)=Pl

divide both sides by l

you get c

please i need help i will give 60 point
and show work

Answers

Is it just me or can anyone else not see the picture?

Answer:

1) 1 1/4

2) 1 3/5

3) 1

4) 2 7/8

5) 1 1/8

6) 1/3

7) C

8) B

9) C

10) A

11) B

12) B

Step-by-step explanation:

Hope this helps fr

How do we determine the area of an a rectangle? ​

Answers

Answer:

accept length

accept breadth

Area=length *breadth

Answer

we multiply the length of a rectangle by the width of the rectangle.

Evaluate a+b+cd if a=7/8 , b=−7/16 , c=0.8 , and d=1/4 . Write your answer as a fraction in simplest form.

Answers

2 I got the one that was in my room and I’m going on a black screen and then I’m watching one

After solving the given expression, the value obtained from it in form of simplest fraction is equal to 5.1/8.

What is an expression?

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given data in the question,

a = 7/8

b = -7/16

c = 0.8 and

d = 1/4

And the equation is a+b+cd

7/8 + (-7/16) + (0.8)(1/4)

7/16 + 0.2

= 10.2/16

In simplest form, it is written as 5.1/8.

To know more about expression:

https://brainly.com/question/14083225

#SPJ2

Hi again could you help me please
Find the area of the composite shape.​

Answers

Answer:

For the one on the far left its 104 m2

Step-by-step explanation:

u split the shape in a square and rectangle

them u fin the area of the square by multiplying both sides. (8*8)

then u find the area of the rectangle by using the formula

2*(16+4)

when u find both areas u count them up and it'll become 104 m squared

6.
Which of the following equations describes the graph?
A. y= -2x^2 - 4
B. y= 2x^2 + 4
C. y= -2x^2 + 4
D. y= 2x^2 - 4

Answers

Answer:

C. y= -2x^2 + 4

Step-by-step explanation:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:  

(

0

,

4

)

Focus:  

(

0

,

33

8

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

31

8

x

y

2

12

1

6

0

4

1

6

2

12

________________

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

(

0

,

4

)

Focus:  

(

0

,

33

8

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

31

8

x

y

2

12

1

6

0

4

1

6

2

12

______________

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:  

(

0

,

4

)

Focus:  

(

0

,

31

8

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

33

8

x

y

2

4

1

2

0

4

1

2

2

4

_______________

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

(

0

,

4

)

Focus:  

(

0

,

31

8

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

33

8

x

y

2

4

1

2

0

4

1

2

2

4

Which is the best way to fix the following run on sentence

Answers

Answer:

C

Reasoning:

You should add a period to fix the run-on sentence because they're two different ideas. (They don't fit in the same sentence.)

James threw a flying disk from a height of 4 feet above the ground. The disk travels a horizontal distance of 30 feet before falling to the ground. the height of the disk, in feet, at a distance of x feet from james, is modeled on the graph.

the domain represents the _____ the flying disk. The range of this function is [___, ___]. for this function, the range represents the flying disk’s _________

Answers

Answer:

the domain represents the horizontal flying of the disk. The range of this function is [0, 7]. For this function, the range represents the flying disk's possible heights

Find the gradient of the line segment between the points (6,-4) and (10,-10). Give your answer in its simplest form.

Answers

Answer:

To calculate the gradient of a straight line we choose two points on the line itself. The difference in height (y co-ordinates) ÷ The difference in width (x co-ordinates).

so it is 0.2

x-4-2=-11
i need help on this asap

Answers

Answer:

X = -5

Step-by-step explanation:

X-4-2=-11

X-6=-11

X=-11+6

X=-5

Hope it helped youuuuu

Someone please help! Thank you in advance!

Answers

Answer:

58ft

Step-by-step explanation:

100-60=40

40+18=58

the answer is 58ft

(brainliest plz)

Ibrar bought a house for £250,000
The value of the house depreciated by 2% in the first year.
The value of the house depreciated by 0.6% in the second year.
Ibrar says,
"2 + 0.6 = 2.6 so in two years the value of my house depreciated by 2.6%"
Is Ibrar right?
You must give a reason for your answer

Answers

Step-by-step explanation:

nope!

because the value has increased 6%*102%=6.12% in second year which we have 8.12% i total

can someone help me with this work problem?
thank you!( ◜‿◝ )♡​

Answers

adddddddddddddddddddddddddddddddddddddddddddddddddddddd

Please help, will mark brainliest!!! :D
btw, you can just answer in A B C D; A is upper left, B is upper right, C is lower left, D is lower right.
THANK YOUUUUUUUUUUUUU

Answers

Answer:

D because that the only that make sense

Step-by-step explanation:

Simplify the expression: – 9k2+6k2–7k2–5k2+ – 8k2+ – 2k2

Answers

Step-by-step explanation:

I guess, this expression really is

-9k² + 6k² - 7k² - 5k² + -8k² + -2k²

remember : all terms with the same base reference (either a number or a variable with the same exponent, or a function ...) can be combined.

all the terms in this expression are about k². so we can combine them all

k² × (-9 + 6 - 7 - 5 - 8 - 2) =

k² × -25 or simply -25k²

always also remember the rules of combining signs and operations :

++ = +

+- = -

-+ = -

-- = +

Jeff decides to ride his bike in the summer, too. At the end of the summer, he has rode his bike for 1,890 minutes. If he rode the same amount every day for 9 weeks, how many minutes did he ride per day? He rode minutes per day.

Answers

Answer:

30 minutes

Step-by-step explanation:

9 weeks = 1890 minutes

=> 1 week = 210 minutes

=> 7 days = 210 minutes

=> 1 day = 30 minutes.

Therefore, he rode 30 minutes per day in the summer.

Answer:

30 min / day

Step-by-step explanation:

Riding total = 1890 min

Number of days:

9*7 = 63

Daily riding:

1890/63 = 30 min

A cylinder has a volume of 33,912 units3 and a
height of 12 units. What is the diameter of the
cylinder?

I’ll do 50 points please answer right away !!!!!!!

Answers

Answer:

60

Step-by-step explanation:

I hope this helps

The diameter of the  cylinder is equal to 59.98 units.

Given the following data:

Volume of cylinder = 33,912 [tex]unit^3[/tex]Height of cylinder = 12 units.

To determine the diameter of the  cylinder:

First of all, we would find the radius of the circular base of this cylinder.

Mathematically, the volume of a cylinder is given by the formula:

[tex]Volume = \pi r^2h[/tex]

Making r the subject of formula, we have:

[tex]r=\sqrt{\frac{V}{\pi h} }[/tex]

Substituting the given parameters into the formula, we have;

[tex]r=\sqrt{\frac{33912}{3.142 \times 12} }\\\\r=\sqrt{899.43}[/tex]

Radius, r = 29.99 units.

For the diameter:

[tex]Diameter = 2 \times radius\\\\Diameter = 2 \times29.99[/tex]

Diameter = 59.98 units.

Read more: https://brainly.com/question/1908836

Solve the following quadratic function by utilizing the square root method. y = x2 - 64​

Answers

Answer:

[tex]x=\pm\sqrt{y+64}[/tex]

Step-by-step explanation:

All you need to do is isolate the x.

First, add 64 to both sides:

[tex]y=x^2-64\\x^2-64+64=y+64\\x^2=y+64[/tex]

Then, take the square root of both sides:

[tex]\sqrt{x^2}=\sqrt{y+64}\\x=\sqrt{y+64[/tex]

Actually, that is:

[tex]x=\pm\sqrt{y+64}[/tex]

Here's the reason for that. An example would be:

[tex]x^2=4[/tex]

Here, you'd take the square root of both sides to solve for x.

[tex]\sqrt{x^2}=\sqrt{4}\\x=2[/tex]

Right? But X could also be a -2, because a negative times a negative is a positive.

[tex](-2)^2=4\\-2\times-2=4\\4=4[/tex]

Therefore, [tex]x=2, -2[/tex] or [tex]x=\pm2[/tex]

[tex]x^2=2\times2=4\\x^2=-2\times-2=4[/tex]

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