Find the limit of the function algebraically.

Find The Limit Of The Function Algebraically.

Answers

Answer 1

Given:

The given limit problem is:

[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}[/tex]

To find:

The value of the given limit problem.

Solution:

We have,

[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}[/tex]

In can be written as:

[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}=\lim_{x\to 0}\dfrac{x^2}{x^4}+\dfrac{3}{x^4}[/tex]

[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}=\lim_{x\to 0}\dfrac{1}{x^2}+\dfrac{3}{x^4}[/tex]

After applying limits, we get

[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}=\dfrac{1}{0^2}+\dfrac{3}{0^4}[/tex]

[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}=\infty+\infty[/tex]

[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}=\infty[/tex]

Therefore, the value of the given limit problem is [tex]\infty[/tex].


Related Questions

In ABC, m∠A=10 and m∠B=145. Select the triangles that are similar to ABC.

Answers

Answer:

A

Step-by-step explanation:

A triangle has 180 degrees.

So, 10 + 145 + x = 180

x = 25

This means that the angles in the triangle are:

10, 145, and 25

Using this information, only A has the same values so it is the answer

Serafine went shopping and bought the following items:
SERAFINE'S SHOPPING LIST
1 loaf bread $2.99
1 jar peanut butter $3.19
3 pounds apples $2.59
She had one coupon for $0.25 off and another for $0.40 off. Which expression represents
the total amount she needs to pay?
A
B
$2.99+ $3.19+ $ 2.59+ $0.25 + $0.40
$2.99 + $ 3.19+ $ 2.59+($0.25 - $0.40)
c$2.99+ $3.19+ $ 2.59+(- 50.25 + $0.40)
$2.99+ $3.19+ $2.59+- $0.25)+(- $0.40)
D

Answers

Answer:

I am going to assume that D's expression is actually $2.99+$3.19+$2.59+(-$0.25)+(-$0.40)

= $6.18+$2.59-$0.25-$0.40 [Note: (+)*(-)=(-)]

=$8.77-$0.25-$0.40

=$8.52-$0.40

=$8.12

Step-by-step explanation:

The prices of the loaf bread, a jar of peanut butter and 3 pounds of apples will be added. The value of the coupons will be then reduced from the total to get the final total.

Please help if you know the answer please

Answers

The answer is 9000 g

Mhnaifa can you please help?

Answers

Answer:

1: 9

2: i dont know sorry

3: 21/2

Step-by-step explanation:

1: know that the bottom portion of the triangle is 18  the bottom left is 12 and the top left is 6. Now you could say that its six because they look the same size but we cant be sure, and six isnt an option. i dont know how to solve so we're using process of elimination so bare with me. we alread have 12 and 18 and theyre way bigger, it cant be 11 because it wouldnt be that small. so in my mind its 9.  

2:  n/A

3: because i said so

Answer:

#1

AQ/QC = AP/PBAQ / 18 = 6 / 12AQ = 18/2AQ = 9

Option D

#2

x/ 12 = 10 / 24x = 12*10/24x = 5

#3

(x - 8)/5 = 2/42(x - 8) = 52x - 16 = 52x = 21x = 21/2

Option B

help?? lols ,,

will mark brainliest, i guess

Answers

Answer:

-80x + 28y - 56

4(-20x + 7y - 14)

Daniel solves the equation 3(x+1)-5=3x-2 and states that it has no solution. Is he correct?
Explain why and why not.

Answers

Answer:

He is incorrect

Step-by-step explanation:

Given

3(x + 1) - 5 = 3x - 2 ← simplify left side

3x + 3 - 5 = 3x - 2

3x - 2 = 3x - 2

Since both sides are equal, then this indicates that the equation has infinite solutions.

On Tuesday the cafeteria sold pizza slices and burritos. The number of pizza slices sold was 20 less than twice the
number of burritos sold. Pizza sold for $2.50 a slice and burritos sold for $3.00 each. The cafeteria collected a total of
$358 for selling these two items. Homework Help
a. Write two equations with two variables to represent the information in this problem. Be sure to define your
variables by writing let statements.
b. Solve your system from part (a). Then determine how many pizza slices were sold.

Answers

Answer:

82

Yes, that is the answer. Try it and you'll get it correct, I think...

For a function,x cannot what?

a) be zero

b)repeat

c)multiply

d) even

Answers

A po ang tamang sagot sana makatulong

Help meeee no Decimal answers.

Answers

Answer: 1,145,375cm^3

Step-by-step explanation:

Answer: Answer in photo below.

Hope this helps!

Find the value of x in the triangle shown below.

Answers

Answer:

x = 61°

Step-by-step explanation:

since the triangle is isosceles the two angles opposite 58° are equal so:

x = (180° - 58°)/2 = 61°

Explain why each statement is true. 5 + 2 + 3 = 5 + (2 + 3)

Answers

Answer:

Associative property of addition. Grouping different addends does not change the sum.

Step-by-step explanation:

5 + 2 + 3 = 5 + (2 + 3)

10 = 5 + (5)

10 = 10

A grocery store recently sold 10 cans of soup, 5 of which were lentil soup. What is the experimental probability that the next can sold will be lentil soup?

Write your answer as a fraction or whole number.



plz halp me

Answers

Answer: the answer is 1/2

Step-by-step explanation: I just got the answer form IXL

Answer:

1/2 is the answer

Step-by-step explanation:

1/2

Classify this triangle by its sides and angles.

Answers

Answer:

choice 3) acute and equilateral

Step-by-step explanation:

Acute + Equilateral

Fiona is seven years less than twice the age of Carlos. The combined age of
Fiona and Carlos is 53 years.
Which of the following systems of equations represents the situation?
A.F= 2C – 7
C+F = 53
B.C= 2F - 7
C + F = 53
C.F = 53 – 7
C + F = 2C

How old is fiona and how old is Carlos

Answers

It’s C. Carlos is 20 and Fiona is 33.

The seagull population on a small island in the Atlantic Ocean can be calculated using the formula

P(t) = 5.3/11/?, where P is the population in hundred thousands, and t is in years. What will the seagull

population on the island be after 5 years? (Round to the nearest tenth.)

a. about 41.6 hundred thousand

c. about 172.4 hundred thousand

about 3.7 x 10' hundred thousand d. about 66.5 hundred thousand

Answers

The correct relation for the sea gull population is: P(t) = 5.3t^(11/7)

Answer:

d. about 66.5 hundred thousand

Step-by-step explanation:

Given that :

P(t) = 5.3t^(11/7)

Population, P is in hujdred thousand ; t = number of years

Population after 5 years ;

t = 5

P(5) = 5.3 * 5^(11/7)

P(5) = 5.3 * 5^1.5714285

P(5) = 5.3 * 12.542422

P(5) = 66.474840

P(5) = 66.5 (approximately)

Hence, population after 5 years will be about 66.5 hundred thousand.

HELP EMERGENCY PLEASE!!!!

Find the percent of children who answered yes to the survey. Find the percent of children who answered no to the survey. Round each answer to the nearest tenth of a percent.

Answers

Answer:

31%

33%

Step-by-step explanation:

I'm not 100% sure. I tried my best.

What fractions that are less than 3/5

Answers

Answer:

1/8 and 1/12

Step-by-step explanation:

Solve for s -5s=−13 .

Answers

Answer:

13/4

Step-by-step explanation:

for these types of problems i recommend symbolab

HELP ASAP!!!! Rosa has 4 1/2 pounds of pizza dough. She uses 3/4 of a pound for one pizza. How many pizzas could be made from Rosa's dough?

Answers

Answer:

6

Step-by-step explanation:

3/4

1 1/2

2 1/4

3

3 3/4

4 1/2

Sorry if this doesn't make sense, I hope I helped though!

2) Find the slope of the line

Answers

assuming each line goes up by 1. we basically need to find a number that goes by rise/run. to get to the next point we need to go up 1, then to the left by 3. notice the slope is negative so we need to add a negative integer.

answer:

-1/3 (C)

hope this helps! :D
Answer is C! Hope this helps

What is the area of these trapezoid

Answers

Answer:

1. 54ft squared  2. 48 cm squared

Step-by-step explanation:

Please help will give brainliest

Answers

Answer:

D

Step-by-step explanation:

40% = [tex]\frac{40}{100}[/tex] = [tex]\frac{2}{5}[/tex] ← in simplest form

Then

[tex]\frac{2}{5}[/tex] of $120 = [tex]\frac{2}{5}[/tex] × $120 = 2 × $24 = $48

she pays $120 - $48 = $72

Someone help me solve all this + include working out.
Will mark as brainliest. Thanks

Answers

Answer:

We know that P(x) = 30*x^3 + k*x^2 + 1

a) If (3x - 1) is a factor, let's find the value of k.

Because the degree of the original polynomial is 3, and the degree of the factor is 1, we should multiply it by a polynomial of degree 2.

Then:

30*x^3 + k*x^2 + 1 = (3*x - 1)*(a*x^2 + b*x + c)

30*x^3 + k*x^2 + 1  = 3*a*x^3 + 3*b*x^2 + 3*c*x - a*x^2 - b*x - c

30*x^3 + k*x^2 + 1 = 3*a*x^3 + (3*b - a)*x^2 + (3*c - b)*x - c

The terms with the same exponent should be equal, then:

30*x^3 = 3*a*x^3

30 = 3*a

30/3 = a = 10

k*x^2 = (3*b - a)*x^2

k = (3*b - 10)  

0*x = (3*c - b)*x

0 = (3*c - b)

b = 3*c

and

1 = -c

then:

c = -1

Replacing this in the equation: b = 3*c

we get: b = -3

Replacing this in the equation for k, we get:

k = (3*b - 10) = (3*-3 - 10) = -19

k = -19

And we can write:

P(x) = (3*x - 1)*(10*x^2 - 3*x - 1)

b) Now we want to write P(x) as a product of its linear factors.

Then we need to factorize the quadratic part:

We need to solve

10*x^2 - 3*x - 1 = 0

We can use the Bhaskara's equation to get the solutions:

[tex]x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*10*(-1)} }{2*10} = \frac{3 \pm 7}{10}[/tex]

Then the two zeros of that polynomial are

x = (3 + 7)/10 = 1

x = (3 - 7)/10 = - 4/10 = -2/5

So we can write the polynomial as:

10*(x - 1)*(x - (-2/5))

Replacing this in the equation of P(x) we get:

P(x) = (3*x - 1)*10*(x -1)*(x + 2/5)

     = 10* (3*x - 1)*(x -1)*(x + 2/5)

So P(x) is written as a product of lineal factors.

C) The zeros of the polynomial are the values of x such that one of the factors becomes equal to zero.

For the first factor, we have a zero at x = 1/3

for the second, we have a zero at x = 1

for the third one, we have a zero at  x = -2/5

ticket to the school play cost $9 for adults and $6 for students. The Smith Family bought 4 adult tickets and 5 student tickets. The Jones family bought 3 adult tickets and 7 student tickets. What was the difference in the amount spent by the two families?

Answers

Answer:

Difference is $3

Step-by-step explanation:

The Jones Family bought 3 adult tickets and 7 student tickets, so they spent 27+42=$69 spent.

The Smith Family bought 4 adult tickets and 5 student tickets, so they spent 36+30=$66 spent.

The difference between them is 69-66=$3.

So, the difference between how much the two families spent is $3.

Answer:

3$

Step-by-step explanation:

Smith family:

9x4=36

5x6=30

total=66$

Jones family:

3x9=27

7x6=42

total=69$

difference=3$

Please help I have been stuck for a while now

Answers

The Answer would be B. Because it would be the same numbers as the original just the sign flipped

PLEASE HELP ASAP
Find the surface area and the volume of the prism.

Answers

Answer:

Surface Area: 1320

Volume: 2160

Step-by-step explanation:

Before calculating Volume and Surface Area, we need to calculate the missing side of the right triangle using the Pythagoreon theorem: [tex]a^2+b^2=c^2[/tex]

where c is the hypotenuse, 26.

Substituting the values into the equation you get:

10^2 + b^2 = 26^2

100 +b^2 = 676

Subtract 100 from both sides.

b^2 = 576

b = 24

Now that we have the missing side, we can calculate the rest of the question.

Surface Area =  2([tex]\frac{1}2[/tex] × 24 × 10) + (18 × 26) + (18 × 24)  +(18 × 10)

240 + 468 + 432 + 180 = 1320 unit^2

Volume = [tex]\frac{1}2[/tex] × base × height × length

[tex]\frac{1}2[/tex] × 24 × 10 × 18 = 2160 unit^2

Brainliest if you don't mind ;)

HURRY 50 POINTS
Which is the correct classification and decimal expansion of StartFraction 5 Over 8 EndFraction?
irrational number, 0.6ModifyingAbove 25 with bar
irrational number, 0.625
rational number, 0.625
rational number, 0.6ModifyingAbove 25 with bar

Answers

Answer:

the correct classification and decimal expansion of StartFraction 5 Over 8 EndFraction

=5/8=0.625[irrational number]

Answer:

The correct answer is (b) i believe

Step-by-step explanation:

   Have a great day!

On the map below, 1⁄4 inch represents one
mile. Candler, Canton, and Oteen are three
cities on the map.

If Candler and Oteen are 3 1⁄2 inches apart
on the map, what is the actual distance
between Candler and Oteen in miles?

Answers

Where’s the map at homie?

Step-by-step explanation:

I got 80% on a major grade. It's not that bad, right?

Answers

Answer:

no, that's good

Step-by-step explanation:

I'm pretty sure that's a b, so it's good

Answer:

No thats good cause last year i had a 60% as my major grade but i got 92% this year

Step-by-step explanation:

please help i’ll give brainliest

Answers

Answer:

Matter in living things may pass into nonliving things.

Step-by-step explanation:

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