test the continuity of
and evaluate.easy question.show your work.​

Test The Continuity Ofand Evaluate.easy Question.show Your Work.

Answers

Answer 1

9514 1404 393

Answer:

  (i) not continuous at x=2

  (ii) -√2

Step-by-step explanation:

(i) The function simplifies to ((x -2)(x+2))/(x -2) = x +2 . . . . x ≠ 2

The left and right limits at x=2 exist and are the same: 4. However, the function is undefined at x=2, so the conditions for continuity are not met.

__

(ii) The expression is indeterminate (0/0) at x=π/4, so  L'Hopital's rule can be used to find the limit.

  lim[x→π/4] = ((d/dx)(cos(x)-sin(x)))/((d/dx)(x-π/4)) = (-sin(π/4)-cos(π/4))/1

  lim[x→π/4] = -√2/2-√2/2 = -√2

The limit is -√2.


Related Questions

The graph below shows the number of tickets that a movie theater sold over a four week period.





If the theater continues selling tickets at the same rate, how many tickets do you predict they will sell during the 6th week?

A. 520 tickets

B. 590 tickets

C. 660 tickets

D. 730 tickets

Answers

it would be 520 because it did the calculations and its right

Answer:

Actually, the correct answer is B: 590.

Step-by-step explanation:

I got right on the test. That's your proof there!

PLZ HELP QUICK NO LINKS

Answers

22 if I’m not mistaken

Answer:

11

Step-by-step explanation:

2 x 11=22

22/2=11

Please help ill mark brainliest if correct
I attached a photo of the problem

Answers

Answer:

12.8

Step-by-step explanation:

imagine a right triangle in the middle,

base: 16 ÷ 2 = 8 cm, height: 10 cm, side: s

10² + 8² = s²

=> s = √(10² + 8²)

=> s = √(100 + 64)

=> s = √164

=> s ≈ 12.8

8.
Which equation best describes the graph? Please give explanation and dont just put anything down for points
Y
A
8
6
4
2
-8
- 6
-4
-2
2
4
6 8
-2
-
y = - 2x + 3
с
y = -3x + }
O y = -fx +
B y = -3.x + 3

Answers

Answer:

A. y = -⅓x + 3

Step-by-step explanation:

Find the equation of the graph bin slope-intercept form, y = mx + b. Where,

m = slope = ∆y/∆x

Using two points on the line, (0, 3) and (3, 2),

Slope (m) = (2 - 3)/(3 - 0) = -1/3

m = -⅓

b = y-intercept = 3 (the y-coordinate of the point where the line crosses the y-axis)

✅To write the equation, substitute m = -⅓ and b = 3 into y = mx + b

Thus:

y = -⅓x + 3

Calvin found census data for the population of Idaho from 1870 through 2000. He made the chart and scatter plot using this
data.
Idaho Population
Calvin's Graph
Yaar
1870
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
1994
2000
2010
TID Pop
18
33
89
162
326
432
445
525
589
667
713
944
1007
1040
1800
1600)
1400
1200
Population 1000
in Thousands 800
600
400
200
OL
1860
1890
1920
1950
Year
1980
2010
Using a line of best fit, which of these would be a reasonable prediction for the population of Idaho in 2020?
O A 1.600.000
O D. 1,000,000
O B. 1,400,000
O E. 800.000
O c. 1.200.000

Answers

Answer:

it’s D

Step-by-step explanation:

Use the Cross Products Property to solve x/35 = 2/7.

Answers

7 times x, 35 times 2
7x=70
divide both sides by 7
x=10

Answer:

x = 10

Step-by-step explanation:

Set up:

[tex]\frac{x}{35} = \frac{2}{7} \\[/tex]

Cross multiple:

7x = 70

Divide by 7

x = 10

A card is drawn from a deck of 52 cards. Find the probability of drawing a black card.

14) Find the probability of drawing a red card.

15) Find the probability of drawing a red or black.

16) Find the probability of drawing an ace.

17) Find the probability of drawing either a jack or queen or king.

Answers

Answer: See below

Step-by-step explanation:

14) 26/52 of the cards are red, 1/2

15) All of the cards are red or black, 1/1

16) 4/52 of the cards are aces, 1/13

17) 12/52 of the cards are J/Q/K, 3/13

Convert the fractions to whatever unit is needed.

Answer:

14) 26/52

15) 52/52

16) 4/52

17) 24/52

Step-by-step explanation:

plzz help im in class RIGHT NOW

Answers

Answer:

i have no answer

Step-by-step explanation:

Answer:

You're a really fungi

Step-by-step explanation:

Match the following.

Answers

Answer:

1) Rotation    

2) Reflection

3)Dilation

4) Rotation

5) Reflection

6) Translation

7) Rotation

Step-by-step explanation: :

Keep in mind

 Reflection is a flip.

Rotation turns a figure through an angle about a fixed point called the center.

Translation "slides" an object a fixed distance in a given direction.

Dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

A scale drawing of a house uses a scale of 0.5 inches = 2 feet what is the length in inches of a line on the scale drawing that represents an actual length of 5 feet.​

Answers

Answer:

We can use ratios for solve this problem

Cross multiply to get:

Lastly, divide both sides by 2 to isolate x

The line will be 1.25 inches

Hope this helps!

P.s. can I get Brainliest?

Find the value of X given 2 angles, 58 and 38.

Answers

Answer:

84

Step-by-step explanation:

180 - 58 - 38 = 84

because all the angles of a triangle add up to 180

Answer: 84

Step-by-step explanation:

A triangles total angles are 180 so we just have to subtract 58+38 from 180

What is the expression resulting from the following diagram?
3x)
Drop Down 1]
-2x-5
[Drop Down 2]
-4/11
[Drop Down 3]
[Drop Down 1)
Select a Value
Drop Down 2]
Select a Value
Drop Down 3]
Select a Value

Answers

Answer:

1. -12x^8

2. 8x^6

3. 16x^11

Step-by-step explanation:

The required values for the given table are -12x⁸, 8x⁶ and 16x¹¹ respectively. To understand the calculations, check below.

Multiplication table:

The given table represents the Multiplication table.

To fill the table we need to multiply the corresponding elements of that cell of the table.

For drop-down 1,

[tex](-4x^{11})\times (3x^{-3})=(-4\times 3)x^{11-3}[/tex]

[tex](-4x^{11})\times (3x^{-3})=-12x^{8}[/tex]

For drop-down 2,

[tex](-4x^{11})\times (-2x^{-5})=(-4\times (-2))x^{11-5}[/tex]

[tex](-4x^{11})\times (-2x^{-5})=8x^{6}[/tex]

For drop-down 3,

[tex](-4x^{11})\times (-4)=(-4\times (-4))x^{11}[/tex]

[tex](-4x^{11})\times (-4)=16x^{11}[/tex]

Therefore, the required values are -12x⁸, 8x⁶ and 16x¹¹ respectively.

Find out more about 'Multiplication table' here:

https://brainly.com/question/17211095

Easy easy easy point easy please explain and make it quick as possible

Answers

Answer:

--

Step-by-step explanation:

so basically when we write all three of the expressions in one fraction we get the same answer for all three multiplications.

a. (3/4)*7=(3*7)/4

b. 7*(3/4)=(7*3)/4

c. 3*(7/4)=(3*7)/4

when we change the place of the values that are being multiplied the value of the multiplication does not change, that's why they will be have the same answer and when we multiply all the operations, we get the same value as the answer.

Answer:

Step-by-step explanation:

so basically when we write all three of the expressions in one fraction we get the same answer for all three multiplications.a. (3/4)*7=(3*7)/4b. 7*(3/4)=(7*3)/4c. 3*(7/4)=(3*7)/4when we change the place of the values that are being multiplied the value of the multiplication does not change, that's why they will be have the same answer and when we multiply all the operations, we get the same value as the answer.

LifeCharge Batteries claims that their batteries last an average of 210 hours when used in a hand held gaming system, with a standard deviation of about 9 hours. An independent quality control company took a sample of 34 batteries, and used the same hand held gaming system that LifeCharge used to record the time the batteries lasted.
1. Assuming the claim is true, what is the probability that the value of the sample mean is greater than 251.7 hours.
2. The sample mean was found to be 251.7, what does this say about the claim?
A. The sample mean is quite far off from the mean claimed, casting doubt on the current mean.
B. The sample mean is sufficiently close to the mean claimed, supporting the current mean.
C. The sample mean found does not truly support nor cast doubt on the current mean.

Answers

Answer:

The answer is "0.0023 and Choice a"

Step-by-step explanation:

In point a:

The central limit theorem:

[tex]\mu_{X}= 250\\\\\sigma_{X}=\frac{\sigma}{\sqrt{n}}=\frac{6}{\sqrt{100}} =0.6\\\\P(\bar{X}>251.7)\\\\=P(z>\frac{251.70-250}{0.6})\\\\=P(z>2.83)\\\\=1-0.9977\\\\=0.0023[/tex]

In point b:

The chance is lower than 0.05. This means that it is very rare to see the average sample above 251.8 if the argument is valid, that is why the means of the sample is far away from the common claimed and casts doubt on the actual mean.

2. You have 15 nickels and dimes. The coins are worth $1.20. How many of each coin do you have?

Answers

Answer:

9 dimes and 6 nickles

Step-by-step explanation:

Find the area of each figure. Please help <3 it would be appreciated! (30 points)

Answers

Answer:

[tex] 1,824 \: {in}^{2} [/tex]

Step-by-step explanation:

Area of the figure = Area of rectangle with dimensions 48 in and 32 in + Area of triangle with base 48 in and height 12 in.

[tex] = 48 \times 32 + \frac{1}{2} \times 48 \times 12 \\ \\ = 1,536 + 24 \times 12 \\ \\ = 1,536 + 288 \\ \\ = 1,824 \: {in}^{2} [/tex]

X^2=4 convert exponential function into natural logarithm (ln)

Answers

Answer:

[tex]2 = ln(4) [/tex]

Step-by-step explanation:

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

Since the power is 2 and our answer is 4 our natural log equation look like

[tex]2 = ln(4) [/tex]

Can someone please help me with just these two thanks I will give a brainliest to the correct answers

Answers

Answer:

7. [tex]c = 15.81[/tex]

8. [tex]b = 16[/tex]

Step-by-step explanation:

Required

Determine the third sides

(7): We have

[tex]b = 5[/tex]

[tex]a = 15[/tex]

[tex]c=??[/tex]

To find c, we make use of Pythagoras theorem

[tex]c^2 = a^2 + b^2[/tex]

[tex]c^2 = 5^2 + 15^2[/tex]

[tex]c^2 = 250[/tex]

[tex]c = \sqrt{250[/tex]

[tex]c = 15.81[/tex]

(8): We have

[tex]c = 20[/tex]

[tex]a = 12[/tex]

[tex]b = ??[/tex]

To find c, we make use of Pythagoras theorem

[tex]c^2 = a^2 + b^2[/tex]

[tex]20^2 = 12^2 + b^2[/tex]

[tex]400 = 144 + b^2[/tex]

[tex]b^2 = 400 - 144[/tex]

[tex]b^2 = 256[/tex]

[tex]b = \sqrt{256[/tex]

[tex]b = 16[/tex]

B.
O
24
10
26
Find tan 2C
A.
5
13
B.
12
13
C. 12
5

Answers

Answer:

=12/5

Step-by-step explanation:

tan<C=opposite/hypotenuse

tan<C=24/10

tan<C=12/5

10 The cost to rent the cabin is $125 per night, plus a $50
non-refundable cleaning fee. Which equation would find the
total cost C of staying at the cabin for n nights?
A C = 125n + 50
B C = 50n + 125
с
n = 125C + 50
D 125
50C +n

Answers

Answer:

C=125n+50

Step-by-step explanation:

each night you stay represents "n" so if you stayed 3 nights(n)

you would multiple 125x3= 375

plus the $50 non refundable charge

Raina received a $90 gift card for a coffee store. She used it in buying some coffee that's cost $7.38 per pound. After buying the coffee, she had $53.10 left on her card. How many pounds of coffee did she buy?

Answers

Answer:

5 lbs

Step-by-step explanation:

90 - 53.10 = 36.90

She spent $36.90 on coffee. Since it cost $7.38 per pound, we can divide the total cost by 7.38 to figure out how many pounds she bought:

36.90 / 7.38 = 5

Raina bought 5 pounds of coffee.

Please help, hard question

Answers

Answer:

6, 24, 96, 384

Step-by-step explanation:

start with 6 and multiply each successive term by 4

Dr Larson saw 1020 patients last year this year the number of patients he saw was 45% lower how many patients did dr. Larson see this year.​

Answers

Answer:

561 patients

Step-by-step explanation:

45 percent of 1020= 459

1020-459=561

WILL GIVE BRAINLIEST!!
If N is the plane of symmetry, click on the graphic to find the figure that is symmetrical with respect to plane N.

Answers

Answer:

thrid one looks right

Step-by-step explanation:

Answer:

The 4th cone

Step-by-step explanation:

Hello, the answer to your question is the 4th cone; the cone with its bottom half facing skyward.  If you are familiar with plane symmetry, this question is fairly simple.  Since the topmost cone has its bottom half facing downward, it would only be logical to choose the cone that forms mirror halves (superimpose) when paired.  

Hope this helps.

Just in case my explanation was too confusing, I'll attach the image of the answer here.  

Feel free to give me brainliest.

9x+10y =1 9x-6y=-15 solve using elimination

Answers

Answer:

I. x = -1

II. y = 1

Step-by-step explanation:

Given the following algebraic expressions;

9x + 10y = 1 .......equation 1

9x - 6y = -15 ......equation 2

To solve using the elimination method, we would subtract eqn 1 from eqn 2.

(9x - 9x) + (-6y - 10y) = (-15 - 1)

0x - 16y = -16

-16y = -16

16y = 16

y = 16/16

y = 1

Next, we would find the value of x;

From eqn 1;

9x + 10y = 1

Substituting the value of y, we have;

9x + 10(1) = 1

9x + 10 = 1

9x = 1 - 10

9x = -9

x = -9/9

x = -1

Please please help me please please help please

Answers

no it is not!!!!!!!!!!!!!!!!!!!!

Branliest to correct answer explain how you got your answer please

Answers

10.7%

possibility to get a blue marker : 4/15

possibility to get a green marker: 6/15

possibility to get a blue then a green: 24/225

= 10.666666%
= 10.7%

Which quadrant contains the terminal side of 320 degrees?

Answers

Answer:

57 degrees

Step-by-step explanation:

Answer:

4th quadrant

Step-by-step explanation:

Since 320∘ lies between 270∘ and 360∘, the angle lies in the 4th quadrant.

Orlando and Ryan are taking measurements related to the installation of a TV tower. Orlando measures a 62° angle of
elevation to the top of the 950 ft TV tower. Find the angle of elevation for Ryan, standing 80 ft farther from the tower than
Orlando. Round answer to nearest tenth.

Answers

Answer:

85 I think

Step-by-step explanation:

85 no explanation

Find the sum: 28,35,42,49,56,63,70

Answers

Answer:

343

Step-by-step explanation:

Big brain calculator work

28 + 35 + 42 + 49 + 56 + 63 + 70 = 343

Answer:

343

Step-by-step explanation:

28+35+42+49+56+63+70          We are asked to find the sum, so we add all the numbers in the series.

28+35+42+49+56+63+70 = 343

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