Find the following limit. Limit of StartFraction StartRoot x + 2 EndRoot minus 3 Over x minus 7 EndFraction as x approaches 7 Which statements describe finding the limit shown? Check all that apply. Multiply by StartFraction StartRoot x + 2 EndRoot + 3 Over StartRoot x + 2 EndRoot + 3 EndFraction. Get x – 1 in the numerator. Get (x -7)(StartRoot x + 2 EndRoot minus 3) in the denominator. Divide out a common factor of x – 7. Calculate the limit as StartFraction 1 Over 6 EndFraction.

ANSWERS: A,D,E

Answers

Answer 1

Answer:

a,d,e

Step-by-step explanation:

Answer 2

In this question, we apply limit concepts to get the desired limit, finding that the correct options are: A, D and E, leading to the result of the limit being [tex]\frac{1}{6}[/tex].

Limit:

The limit given is:

[tex]\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7}[/tex]

If we apply the usual thing, of just replacing x by 7, the denominator will be 0, so this is not possible.

When we have a term with roots, we rationalize it, multiplying both the denominator and the denominator by the conjugate.

Multiplication by the conjugate:

The term with the root is:

[tex]\sqrt{x+2} - 3[/tex]

It's conjugate is:

[tex]\sqrt{x+2}+3[/tex]

Multiplying numerator and denominator by the conjugate, meaning option A is correct:

[tex]\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7} \times \frac{\sqrt{x+2}+3}{\sqrt{x+2}+3}[/tex]

We do this because at the numerator we can apply:

[tex](a+b)(a-b) = a^2 - b^2[/tex]

Thus

[tex]\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7} \times \frac{\sqrt{x+2}+3}{\sqrt{x+2}+3} = \lim_{x \rightarrow 7} \frac{(\sqrt{x+2})^2 - 3^2}{(x-7)(\sqrt{x+2}+3)} = \lim_{x \rightarrow 7}\frac{x+2-9}{(x-7)(\sqrt{x+2}+3)} = \lim_{x \rightarrow 7}\frac{x-7}{(x-7)(\sqrt{x+2}+3)}[/tex]

Thus, we can simplify the factors of x - 7, meaning that option D is correct, and we get:

[tex]\lim_{x \rightarrow 7} \frac{1}{\sqrt{x+2}+3}[/tex]

Now, we just calculate the limit:

[tex]\lim_{x \rightarrow 7} \frac{1}{\sqrt{x+2}+3} = \frac{1}{\sqrt{7+2}+3} = \frac{1}{3+3} = \frac{1}{6}[/tex]

Thus, option E is also correct.

Using a limit calculator, as given by the image below, we have that 1/6 is the correct answer.

For more on limits, you can check https://brainly.com/question/12207599

Related Questions

FIRST CORRECT ANSWER GETS BRAINLIEST!!!!!!!! Suppose you were digging at a rate of 10 feet per day. Assume you are ar sea level when you begin digging. If there are 365 days in a year, write an equation to represent the depth of the hole where d= depth in feet and t= time in years

Answers

Answer:

simple

Step-by-step explanation:

365 x 10 = 3650 feet

took you 1 year

and adding on sea level 1,312 feet

3650 + 1,312 = 4962 in 1 year

hope im right

If you walk around a circular path TWICE, and the circle has a diameter of 100 m, how far did you walk in TOTAL?

Answers

Answer:

628.32 m

Step-by-step explanation:

C = πd

C = π*(100m)

C = 314.16 m

Total Distance = 2*C

2*C = 628.32 m

Leave a like and brainist if this helped

please help i will give brainliest.

Answers

Answer:

754 ft²

Step-by-step explanation:

Given

d = 24 fth = 4 ft

Required amount of vinyl:

πdh + πd²/4 =3.14*24*4 + 3.14*24²/4 = 754 ft² (rounded)

Figure A ~ Figure B
Find the volume of Figure A

Answers

9514 1404 393

Answer:

1 m³

Step-by-step explanation:

The ratio of volumes is the cube of the ratio of corresponding linear dimensions.

Va/Vb = ((2 m)/(8 m))³ = (1/4)³ = 1/64

Va = Vb(1/64) = (64 cu. m)/(64) = 1 cu. m

The volume of figure A is 1 m³.

in the first box is 1 and the second one is 3

Question 7 of 8
Calculate the amount of interest earned on a $7,500 investment made for 2 years at
5.5% p.a..

Answers

Answer:

$825

Step-by-step explanation:

Formula we use:

I = Prt

Given:

P = 7500

r = 5.5% or 0.055

t = 2

Work:

I = Prt

I = 7500(0.055)(2)

I = 412.5(2)

I = 825

3. Maxine has assets worth $145,000 and liabilities totaling $75,000. What is Maxine's net worth?
A $155,000
B-$15,000
C $70,000
D-$85,000

Answers

Answer: C.) $70,000

Explanation:
Assets - Liabilities = Net worth
$145,000 - $75,000 = $70,000

It would be C

145,000- 75,000=70000

true or false: sin 50* = sin 130*

Answers

Answer:

True

Step-by-step explanation:

sin(130)

sin(180-50)

By difference rule for sine

sin(180)cos(50)-sin(50)cos(180)

0*cos(50)-sin(50)*-1

0+sin(50)

sin(50)

The answer is true.

A crate contains 100,000 sheets of paper.
If the crate has a mass of 357,100 gm, what is the mass of
a single sheet of paper?

Answers

Answer:

3.571 g

Step-by-step explanation:

357,100 / 100,000 = 3.571

Answer:

3.571g

Step-by-step explanation:

357100 grams / 100000 sheets of paper = 3.571g per sheet of paper

Please help this is due in 5 minutes. Choose one of the answer to respond to

Answers

Answer:

Option 2

Step-by-step explanation:

I agree with this statement. Biodiversity indicates the health of the ecosystem. Maintaining biodiversity can provide clean air, water, pollination of plants, pest control, food, and keep everything in balance. It can also reduce the impact of natural disasters! One example is a flood.

Answer:

Option 1

Step-by-step explanation:

I do agree with this statement because without matter, we wouldn't have anything. Matter is weight and anything physical.

Kala received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.58 per pound. After buying the coffee, she had 18.52 left on her card. How many pounds of coffee did she buy?

Answers

She bought 6 pounds of coffee. 6 x 8.58 = 51.48. If you add the 18.52 to 51.48 you would get the original $70 she had on the gift card

i need help now please

Answers

Answer:

Step-by-step explanation:

A = ½(b1 + b2)h

A = (3 + 5)(3)/2

A = 12

Hi can I get a thanks I’m also sure A=12!!!!!

Which problem can be solved with 56 + 7 = 8?
Chloe has 56 pennies. Her brother has 7 times as
many pennies as she has, How many pennies does
her brother have?
Chloe has 56 pennies. She finds 7 more pennies.
How many pennies does she have now?
Chloe has 56 pennies. She puts the pennies into
equal stacks of 7. How many stacks does she make?
Chloe has 56 pennies. She gives away 7 pennies.
How many pennies does she have left?

Answers

Answer:

she puts the pennies into equal stacks

Step-by-step explanation:

I think you meant 56 DIVIDED by 7=8, not 56 PLUS 7=8

Answer:

C.Chloe has 56 pennies. She puts the pennies intoequal stacks of 7. How many stacks does she make?

Step-by-step explanation:

( a) Find the lateral area (in square meters) of the prism.
(b) Find the total area (in square meters) of the prism. (Round your answer to three decimal places.)
(c) Find the volume (in cubic meters) of the prism. (Round your answer to three decimal places.)

Answers

Answer:

( a) Find the lateral area (in square meters) of the prism.

answer:

the lateral area=perimeter of triangle ×height=

(4+5+6)×8=120m²

(b) Find the total area (in square meters) of the prism. (Round your answer to three decimal places.)

answer:

total surface area=lateral surface area +2crossed section area=120+2×(1/2×4×5) =120+20=140m²

volume of prism=area of base×height=1/2×4×5×8=80m³

please help with this problem

Answers

Answer:

choice 1) 0, -4/5

Step-by-step explanation:

1/(t² + t) = 1/t - 5

multiply both sides of the equation by (t² + t):

1 = (t² + t)/t - 5t² - 5t

1 = t + 1 - 5t² -5t

-5t² - 4t = 0

t(-5t - 4) = 0

t = 0

-5t = 4

divide both sides by -5:

t = -4/5

someone please help. this is the rest of my points. and it's worth 50% of my grade

Answers

Answer:

a=52

b=128

r=s=100

Step-by-step explanation:

4+4 for 100 points brainlyist to first answer

Answers

Answer:

Step-by-step explanation:

plz me

Answer:

4+4=8

Step-by-step explanation:

.................

Dividend and divisior with quotient 32000 using powers of 10

Answers

Answer:

320,000/10=32000

Step-by-step explanation:

Six years ago Matt was four times as old as Brown, and in 3 years the sum of their
ages will be 43 years. Find their present ages.

Answers

Answer:

Matt=26

Brown=11

Step-by-step explanation:

Just trust me!!!

The present age of Matt given the information in the question is 26.

The present age of Brown given the information in the question is 8.

What are the linear equations that represent the question?

4y - 6 = x equation 1

x + y + 6 = 43 equation 2

Where:

x = Matt's agey = Brown's ageWhat is Brown's age?

Subsistute for x in equation 2

4y - 6 + y + 3 = 43

Combine similar terms

5y = 40

y = 8

What is Matt's age?

Subsitute for y in equation 1

4(8) - 6 = x

32 - 6 = 26

To learn more about simultaneous equations, please check: https://brainly.com/question/25875552

Mathematical Literacy , What does a basic fee mean?

Answers

Answer:

Basic Fee means the compensation provided to Construction Manager for providing Basic Services. ＋ New List. Basic Fee means the compensation provided to Pre-Construction Contractor for providing Basic Services.Step-by-step explanation:

The initial value of a product or service which calls for a fee. Typically this will be understood as the y-intercept in a linear equation.

A man borrowed $8000. He paid $10100 after 9 months for the debt. What was the interest rate per annum?

Answers

Answer:

3.5%

Step-by-step explanation:

Interest = 10100 - 8000 or 2100

I = Prt

2100 = 8000(9/12)r

2100 = 600r

2100/600 = r

3.5 = r

F(x) = xlnx/x+1
Find the derivative

Answers

Answer:

ln(x)

Step-by-step explanation:

if you need the steps .. it's very long... but the answer is easy

ln(x)

How many if there are 2 is the of the is?
How are they related?
Is there a number that can become them?
Find the value of are.

Answers

yes i and i did not answer

Answer: no their is not a number that comes before the value

Step-by-step explanation:

Solve: 1/3(−6q+4)=−1/12(4q+4)

Answers

Answer:

Combine multiplied terms into a single fraction

13(−6+4)=−112(4+4)

13(−6q+4)=−112(4q+4)\frac{1}{3}(-6q+4)=\frac{-1}{12}(4q+4)31(−6q+4)=12−1(4q+4)

1(−6+4)3=−112(4+4)

1(−6q+4)3=−112(4q+4)\frac{1(-6q+4)}{3}=\frac{-1}{12}(4q+4)31(−6q+4)=12−1(4q+4)

Multiply by 1

Combine multiplied terms into a single fraction

Distribute

Multiply all terms by the same value to eliminate fraction denominators

Cancel multiplied terms that are in the denominator

Distribute

Subtract

161616

from both sides of the equation

Simplify

Add

4q4q4q

to both sides of the equation

Simplify

Divide both sides of the equation by the same term

Simplify

Show less

Solution

Step-by-step explanation:

Answer:

q=1

Step 1: Simplify both sides of the equation.

Step 2: Add 1/3q to both sides.

Step 3: Subtract 4/3 from both sides.

Step 4: Multiply both sides by 3/(-5).

The volume of the polyhedron is ______ yd3.

Answers

Answer:

122,850 yd³

Step-by-step explanation:

The polyhedron is a right triangle prism

Area of the right triangle prism = ½*a*c*h

a = 91 yd

c = 60 yd

h = 45 yd

Volume = ½*91*60*45

= 122,850 yd³

The sales tax for an item was $27.20 and it cost $340 before tax.

What is the sales tax rate?

Write your answer as a percentage.

Answers

Answer:

Step-by-step explanation:

27.20/340=0.08

=8%

a sunglasses store bought $5,000 worth of glasses the store made $9,000 making a profit of $20 per sunglasses there were How many pairs of sunglasses involved?

Answers

Answer:

150 pairs

Step-by-step explanation:

so total money spent Is equal to 5000

profit is equal to 3000

profit on each pair is equal to 20

so 3000 divided by 20

which gives 150

so 150 pairs of sunglasses were involved

pls give me brainliest I need it

Answer:

The sunglasses involved are 200

There are two spinners containing only white and green slices. Spinner A has 4 white slices and 1 green slice. All the slices are the same size. Spinner B has 3 white slices and 9 green slices. All the slices are the same size. Each spinner is spun. List these events from least likely to most likely. Event : Spinner B lands on a green slice. Event : Spinner A lands on a white or green slice. Event : Spinner A lands on a white slice. Event : Spinner B lands on a yellow slice.

Answers

Answer:

Step-by-step explanation:

Ok, lets list the important things

only green and white slicesall slices same sizespinner A has 4/5 white slices and 1/5 green slicesspinner B has 3/12 white slices and 9/12 green slices

The 4 options are:

spinner B lands on a green slicespinner A lands on a white or green slicespinner A lands on a white slicespinner B lands on a yellow slice

We already know that choice 2 is 100% probable and option 4 is 0% probability, because in option 2, the spinner A ONLY has white or green slices so the spinner must land on the slice. In option 4, no matter which spinner is spun no yellow slices are available to land on.

the chance of option 1 happening is 9/12 which is 3/4 which is 75%

the chance of option 3 of happening 4/5 which is 80%

option 1 has a 75% chance

option 2 has a 100% chance

option 3 has an 80% chance

option 4 has a 0% chance

this means that the order is:

1. option 4

2. option 3

3. option 1

4. option 2

because it is least likely to most likely.

hope this helped you out and if you need any questions feel free to ask

good luck in maths!

-cheesetoasty

Megan got paid $2,156 for babysitting this year. If she makes $11 an hour, how many hours did she babysit this year

Answers

Answer:

she worked 196 hours

Step-by-step explanation:

just divide 2156 by 11 :p i hope im right lol.

Answer:

196 hours

Step-by-step explanation:

$2156÷$11=196 hours

What is the first step to solve this equation:
11 - 3x = 44

Add 3 to both sides

Add 11 to both sides

Subtract 11 from both sides

Divide 3 on both sides.

Answers

Substracs 11 from both sides

Which function shows the function f(x) = 3^x being
translated 5 units to the left?
A. f(x) = 3^x – 5
B. f(x) = 3^(x+5)
C. f(x) = 3^(x - 5)
D. f(x) = 3^x + 5

Answers

Answer:

Step-by-step explanation:

When you want to move a function on a graph from left to right, you "move" the x, and when moving the x; it's the opposite. So, C would move the function 5 units to the right because it is subtracting.

The correct option will be f(x) = 3^(x - 5)

What is translation?

A translation is a transformation that moves every point in a figure the same distance in the same direction.

Given that, the function f(x) = 3ˣ, being translated 5 units to the left.

Since, the function is being translated in left, therefore, we subtract 5 from x,

i.e. f(x) = 3⁽ˣ⁻⁵⁾

Hence, f(x) = 3⁽ˣ⁻⁵⁾ is the function shows the function f(x) = 3ˣ being

translated 5 units to the left.

For more references on translation, click;

https://brainly.com/question/12463306

#SPJ2

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