in general, if lim x->a m(x) does not exist and lim x->a n(x) does not exist, is it true that lim x->a [m(x) n(x)] does not exist?

Answers

Answer 1

The claim is untrue because, in the case of discrete functions, the absence of either function limit does not imply that the limit product of those two functions will also not exist.

What exactly are limit functions?

When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches. When a variable approaches its limit from the left, the function's left-hand limit is the value that approaches. The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input. Below are formal definitions that were initially developed in the early 19th century. Informally, a function f gives each input x an output f(x). The limit of a constant multiplied by a function is the same as the limit of the function multiplied by the constant. A product's limit is equal to the product of its limits. A quotient's limit is the same as the quotient of its limits. A constant function's limit is the same as the constant.

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Related Questions

there are only 6 blue pens 5 green pens and 8 red pens in a box one pen is taken randomly from the box write down the probability that this pen is blue

Answers

Answer:

6/19

Step-by-step explanation:

19 = total pens (blue pens + green pens + red pens)

6 = total number of blue pens

the number of bacteria in a culture is increasing according to the law of exponential growth. after 3 hours, there are 400 bacteria, and after 6 hours, there are 3,200 bacteria. write an equation that can be used to determine the number of bacteria y in the culture after t hours.

Answers

The number of bacteria y in the culture after x hours will be y = 50(2)ˣ.

What is exponential growth ?

An exponential function faster and faster after every next value of the independent variable.

According to the given question the number of bacteria in a culture is increasing according to the law of exponential growth. after 3 hours, there are 400 bacteria, and after 6 hours, there are 3,200 bacteria.

We use the exponential growth equation y = arˣ where a is the initial value and r is common ratio and x represents time.

so 400=ar^3...(i)  and 3200= ar^6...(i)

Dividing equation (ii) by equation (i) and solve for r we get r³ so r =2

substitute r into first equation 400=a(2)³

8a = 400.

a = 50.

∴ The no. of bacteria at any given time x will be.        ( t is replaced by x)

y = 50(2)ˣ.

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answer the question in the image

Answers

The answer I’m pretty sure is 14/33

Answer:

[tex]\frac{211}{500}[/tex]

Step-by-step explanation:

[tex].4\bar{2}[/tex]  means the 2 repeats till infinity
[tex].4\bar{2}[/tex]  = .4222222222.....

To convert to fraction just take the first three decimal place digits 422 and divide by 1000 to convert to fraction

[tex].4\bar{2} = \frac{422}{1000}[/tex]

Dividing numerator and denominator of this fraction by 2 gives
[tex]\frac{422/2}{1000/2} =\frac{211}{500}[/tex]

This cannot be simplified further and therefore
[tex].4\bar{2} = \frac{211}{500}[/tex]

If we had chosen first 4 decimal digits then it would be[tex].4\bar{2} = \frac{4222}{10000} = \frac{2111}{5000}[/tex]
i.e. we divide by 10,000

please help its a proof question look at the image

given triangle ABC, prove CE=1/2 BD

Answers

use this formula and solve the question

AREA OF BASE = 1 by 2 ×base × Height

4 divided by 8/9 - 1/2

Answers

Answer:

-0.28

Step-by-step explanation:

4 ÷ 8/9 -1/2

BODMAS

8/9 ÷ 4

8/9 x 1/4

2/9 x 1

2/9 - 1/2

= -0.2777

= -0.28

what is -1 3/10 + (-3.8)? show your work

Answers

Answer:

-1 3/10 + (-3.8) = -5.1

Step-by-step explanation:

First 4 solve for x


Last 4 solve for x AND y

Answers

Step-by-step explanation:

find the value of 8x³-y³if 2x-y and xy=-1

Can someone help me

Answers

The given table of the values of f(x) is used to complete the table for the function [tex]y = f \left( \frac{1}{5} \cdot x \right) [/tex], to give;

The following values of x and y as follows;

x: -0.8, -0.2, 0, 0.6, 1.2

y: 7, -2, 3, -4, 5

Please also see the attached table

How can the function, f(x) be scaled to give the function, [tex]y = f \left( \frac{1}{5} \cdot x \right) [/tex]?

The question is with regards to scaling a graph horizontally.

Using the rule of scaling a graph, we have;

Given that a point on the graph of f(x) is (x, y), the corresponding point in the graph of f(C•x) is (C•x, y).

The given modification of the function is presented as follows;

[tex]y = f \left( \frac{1}{5} \cdot x \right) = f \left( 0.2 \cdot x \right)[/tex]

The points on the graph that completes the table are therefore;

(0.2×(-4), 7) = (-0.8, 7)

(0.2×(-1), -2) = (-0.2, -2)

(0.2×0, 3) = (0, 3)

(0.2×3, (-4)) = (0.6, -4)

(0.2×6, 5) = (1.2, 5)

The completed table is therefore;

x y

-0.8 7

-0.2. -2

0 3

0.6. -4

1.2. 5

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find the number represented by the prime factorization 2^3 10^2

Answers

Answer:800

Step-by-step explanation:

2×2×2×10×10=800

Answer:

2^3*3^2=72

Step-by-step explanation:

25 POINTS AND BRAINLIEST
NO EXPLANATION NEEDED JUST ANSWER

Answers

Answer: 35.

Step-by-step explanation: 33 + 34 + 35 is 102. Your 35 is the largest of the three.

the product of a four and a number minus 10.​

Answers

Answer:
14


Explanation:

14 - 10 = 4

the product is 4 and its a number thats subtracting 10

[tex]- \sqrt{64}[/tex]

Answers

The value of the square root of 64 is -8

Square root integers

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

The square root of a number is the values that will can multiply twice to give the resulting value in the root.

Given the expression below:

- √64

Since the square root of 64 is 8, hence;

-√64 = -1 * √64

-√64 = -8

Hence the value of the square root of 64 is -8

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1.5.PS-21 Challenge Yossi used to have a square garage with 314 ft² of floor space. He recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side? One side of the garage was originally 17.7 ft long. (Round to the nearest tenth as needed.) ft long. Question Help One side of the garage is now (Round to the nearest tenth as needed) Enter your answer in the answer box and then click Check Answer. -​

Answers

Required values:

The length of one side of the garage was originally 17.7 ft long

The length of one of the sides of the garage is now 21.7 ft long

The percentage increase in length is 22.5%.

Given parameters are;

The area of the square garage is 314 ft.²

The area of the new garage has 50% more space

Required;

Initial side length:

The initial side length, given to the nearest tenth, s, is the square root of the area, A, given as follows;

s = √(314 ft.²) ≈ 17.7 ft.

New Side length:

The side was increased by 50%, to give,

314 + 0.5×314 = 471

The new area of the garage = 471 ft.²

The side length of the new garage, s = √(471) ≈ 21.7 ft

The side of the garage now is 21.7 ft.

Percentage increase in length:

The percentage increase is given as follows;

% increase in length

= new side length - old side length / old side length * 100  

= 21.7 - 17.7 / 17.7 *100

= 22.5 %

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Evaluate a + b² if a = -3 and b = 6.
117

Answers

Answer: 33

Step-by-step explanation:

(-3)+(6)^2

-3+36

33 (Answer)

-4x+1.5x-2.5x-2 x-6.5= evaluate the expression when x=4

could someone do this :(

Answers

Answer:

-34.5

Step-by-step explanation:

Put together like terms:

-7x-6.5

-28-6.5

-34.5

The marine center has 150 parking spaces in front of its building.

What is the reciprocal of 150?

Answers

The reciprocal of 150 will be 1/150.

We have a marine center has 150 parking spaces in front of its building.

We have to find the reciprocal of 150.

What do you understand by the reciprocal of a number ?

The reciprocal of a number is a number such that the product of both the numbers is equal to 1. Mathematically, if the original number is a, then its reciprocal will be 1/a , such that -

a x 1/a = 1

According to the question -

Let us assume that  A = 150

Now, from the definition of reciprocal, the reciprocal of A will be -

1/A. Therefore, the reciprocal of 150 will be = 1/150

Hence, the reciprocal of 150 will be 1/150.

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one morning each member of angela's family drank an 8-ounce mixture of coffee with milk. the amounts of coffee and milk varied from cup to cup, but were never zero. angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. how many people are in the family?

Answers

There are 5 people in the family.

What is Ratio?

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have been given that each member of angela's family drank an 8-ounce mixture of coffee with milk.  

Let the number of people would be n.

And a represents the coffee, and  b represents the milk,

One-quarter of the milk and one-sixth of the coffee was consumed by Angela.

⇒ Angela drank b/4 of milk and a/6 of coffee.

Since everyone drank the same amount of coffee,

We have been to create an equation as

⇒ (a/6 + b/4)p = a + b

⇒ 2a(6 - n) = 3b(n - 4)

Given that both a and b are positive, we must fulfill the condition.

⇒(6 - n) > 0 and (n - 4) > 0

⇒ 6 > n and n > 4

So, the correct number of people = 5.

Hence, there are 5 people in the family.

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During a snowstorm, Snowfill an a constant rate for a number of hours. Then it stoped snowing for a number of hours. then it started Up again at a different constant rate Andrew Madie graph showing the edges of the snow on the ground over time using the data he collected. After how many hours were there 7 inches of snow on the ground

Answers

Answer: Unable to answer

Step-by-step explanation: If you do not show what the constant rate is, I am unable to solve it for you.

help a real one out i need help with this

Answers

1. A(2,8)  A'(6,7)

2. B(5,2) B'(9,1)

3. C(2,2) C'(6,1)

4. P(x,y) P'(x ₊ 4 , y ₋ 1)

5. x units to x ₊ 4 units.

   y units to y ₋ 1 units.

6. triangle A'B'C' (6 , 4)

7. triangle A'B'C' (7 , 5)

8. triangle ABC ( 3,2)

9. triangle ABC (4 , 4)

Given,

A set of values called coordinates helps to display a point's precise location in the coordinate plane.

we can observe the points from the graph we get the values for B' and C'.

P(x,y) P'(x₊,y₋)

P(2,5) P'=(6,4) ⇒(2₊4,5₋1)

P(3,6) P' = (3₊x' , 6₋y')  ⇒ (3₊4 , 6₋1) = (7,5)

P'(7,1) P = (x'₋4 , y'₊1)  ⇒ (7₋4 , 1₊1) = (3,2)

P'(8,3) P =  (x'₋4 , y'₊1) ⇒ (8₋4 , 3₊1) = (4,4)

hence we acquired the desired values of the points from the graph given.

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how to work out 2x>7

Answers

Answer:

[tex] \: \: \: \: \: \: \: \bf\implies \: x > \frac{7}{2} [/tex]

Step-by-step explanation:

[tex] \tt \mapsto2x > 7 \\ \tt \mapsto 2x = 7 \\ \ \ \tt \mapsto x = \frac{7}{2} \\ \tt \mapsto x > \frac{7}{2} [/tex]

A line with a slope of 1 passes through the point (6,8). What’s it’s equation in slope intercept form?

Answers

Step-by-step explanation:

using y=mx+c (equation of a line)

equation of one point form

y-y1=m(x-x1)

where y1=8,x1=6,m=1

y-8=1(x-6)

y-8=x-6

y=x-6+8

y=x+2

intercept form=2

or

y=mx+c where y=8,x=6,m=1

8=1(6)+c

8=6+c

8-6=c

2=c

or c=2

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Solve for × 3×+2=32

Answers

Answer: x = 10

Step-by-step explanation:

3(10) = 30 +2 + 32

The graph below represents how much money Lana will make babysitting in one night. How much money will Lana make at the start of the night?

Answers

i think its 8. is the x days and y money?

A rectangular swimming pool is 15 meters long, 14 1/2 meters wide, and 5 1/2 meters deep. What is its volume?

Answers

Answer:

length x width x height (or depth) = volume

Step-by-step explanation:

761.25 or 761 1/4 is the answer

Three lakes lost water during a drought. lake jensen lost one sixth of its water, lake parlow lost 26% of its water, and lake stockton lost thirty three two hundredths of its water. which lake lost the least amount of water?

Answers

If three lakes lost water during a drought, lake Jensen lost one-sixth of its water, lake Parlow lost 26% of its water, and lake Stockton lost thirty-three two-hundredths of its water, then the lake that lost the least amount of water is lake Stockton.

The lake that lost the least amount of water can be determined by converting the amounts lost by each of the lakes into percentage form.

As lake Jensen lost one-sixth of its water, it can be written in percentage form as,

Lake Jensen = 1/6 × 100 = 100/6 = 16.67 %

As given, Lake Parlow lost 26%

Lake Parlow = 26%

As Lake Stockton lost thirty-three two-hundredths, it can be written in percentage form as,

Lake Stockton = 33/200 × 100 = 0.165 ×  100 = 16.5 %

Thus, the least percentage of water lost is 16.5% by lake Stockton.

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What is the difference of the two polynomials?

(7y2 + 6xy) – (–2xy + 3)

7y2 + 4xy – 3
7y2 + 8xy – 3
7y2 + 4xy + 3
7y2 + 8xy + 3

Answers

Answer:

7y2 + 8xy - 3

Step-by-step explanation:

7y2 + 6xy + 2xy -3  You distribute the - sign through the second binomial.  You are distributing or multiplying (-2xy -3) by -1  Combine like terms

7y2 + 8xy -3

Answer:

What is the difference of the two polynomials?

(7y2 + 6xy) – (–2xy + 3)

7y2 + 4xy – 3

7y2 + 8xy – 3 Correct

7y2 + 4xy + 3

7y2 + 8xy + 3

Step-by-step explanation:

Write an equation in point-slope form

Answers

Answer:

y = -4/3x + 2

Step-by-step explanation:

Point slope form is this:

y - y1 = m (x - x1)

Where m is the slope. y1 and x1 are where you put your coordinates.

so now we just plug it in.

y - (-2) = -4/3 (x - 3)

We should clean it up in order to make it look like this equation:  y = mx + b

y + 2 = -4/3x -4/3(-3)

y + 2 = -4/3x + 4

y = -4/3x + 2

Given x is the midpoint of line WY, wx is congruent to xz

Prove line xy is congruent to line xz

Give statements and reasons

Answers

The two column proof is completed by the substitution property of equality, which gives;

WX = XZ

XY = XZ

[tex] \overline{XY} \cong \overline{XZ}[/tex]

How can the congruency of the required segments be proven?

The completed two column table is presented as follows;

Statement. Reasons

1. X is the midpoint of [tex] \overline{WY}[/tex]. 1. Given

2. WX = XY 2. Definition of midpoint

3. [tex] \overline{WX} \cong \overline{XZ}[/tex]. 3. Given

4. WX = XZ 4. Definition of midpoint

5. XY = XZ 5. Substitution property of equality

6. [tex] \overline{XY} \cong \overline{XZ}[/tex] 6. Definition of congruency

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How many times larger is (1.092 × 101) than (7 × 10−1)?

Answers

The number 1.092 × 10¹ is 15.6 times larger than  7 × 10⁻¹ .

A number is said to be in standard form if it can be written in a decimal number between 1.0 and 10.0 multiplied with power of 10.

For Example: 1.8x10² is a standard form .

In the given question

1.092×10¹   and    7×10⁻¹

both the numbers are in a standard form

For comparison we need to convert them in decimal form

1.092 × 10¹ = 1.092 x 10 = 10.92

7 × 10⁻¹ = 7/10 = 0.7

So , According to the question

Let 10.92 be x times larger than 0.7

which means

(0.7)*x=10.92

x=10.92/0.7

x=15.6

Therefore , 1.092 × 10¹ is 15.6 times larger than  7 × 10⁻¹ .

The given question is incomplete , the complete question is

How many times larger is (1.092 × 10¹) than (7 × 10⁻¹)?

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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 = g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could
be true for g.
(0)=2
B. 8-13) 20
C. 87)=-1
D. (-4)=-1

Answers

From the given statements, g(-13) = 20, that is option B, is true for g.

Here we are given that a function g has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45.

Further, g(0) = -2 and g(-9) = 6

Let us evaluate each option one by one-

A. g(7) = -1

As we can see x can take values only from -20 to 5. And 7 is greater than 5. This means that the function us not defined at g(7) and hence, option A is not the correct option.

B. g(-13) = 20

Here, x=-13 is in our domain and y = 20 also lies within our range. Hence, this is the correct option.

C. g(0) = 2

We are already given that g(0) = -2. y can take only one unique value for every value of x and hence, g(0) cannot be equal to 2.

D. g(-4) = -11

As we can see y can take values only from -5 to 45. And -11 is smaller than 5. This means that the function us not defined at g(-4) and hence, option D is not the correct option.

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Your question was incomplete. Check for the full content below-

Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.

g(0) = 2

g(7) = -1

g(-4) = -11

g(-13) = 20

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