you may have found the limit from one side instead of from both sides as notated. how might you consider the limit as x approaches a from both sides?
Answers
LHL is equal to RHL then limit exist
LHL is not equal to RHL then limit does not exist.
As per the given data the graph of the function is given
Here we have to determine the limit at the indicated value of a, if it was exists.
You may have found the limit from one side instead of from both sides as notated.
Now we have to find:
[tex]$\lim _{x \rightarrow a} f(x)$[/tex] when a = 1
We find the left hand side limit and the right hand side limit at a = 1
So,
The Left hand limit is [tex]$\lim _{\mathrm{x} \rightarrow 1^{-}} \mathrm{f}(\mathrm{x})=\frac{3}{2}$[/tex]
The Right hand limit is [tex]$\lim _{x \rightarrow 1^{+}}[/tex] f(x) = 3
Here [tex]$\lim _{x \rightarrow 1^{-}} f(x) \neq \lim _{x \rightarrow 1^{+}} f(x)$[/tex]
Hence [tex]$\lim _{x \rightarrow a}[/tex] f(x) = DNE
From the graph we find the left hand limit and the right hand limit:
If Left hand limit = Right hand limit then limit exist
If then Left hand limit ≠ Right hand limit then limit does not exist.
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Use the graph of the given function f to determine the limit at the indicated value of a, if it exists.(If an answer does not exist, enter DNE.)
Graph attached at the end of solution
you may have found the limit from one side instead of from both sides as notated. how might you consider the limit as x approaches a from both sides?
Related Questions
jill is taking 5 courses (or 15 credit hours). how many hours of homework should she expect each week in addition to her time spent inside the classroom?
Answers
Jill should expect an additional 30 to 45 hours of homework each week.
As a general rule of thumb, students can expect to spend 2-3 hours of homework for each hour spent in class. This means that for a 15 credit hour course load, Jill can expect to spend an additional 30 to 45 hours on homework each week.
However, this is just a rough estimate and the actual amount of time required will depend on the difficulty of the courses, the teaching style of the instructors, and the individual study habits and ability of the student. Additionally, some courses may require more time spent on projects, reading, or other assignments that are not factored into this estimate.
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Using the slope intercept form what is the equation of the line: m= 1/4
y-intercept= (0,-2)
*
Answers
Answer: Y=1/4x-2. slope intercept form is y=mx+b
we have our b and our m and that’s all we need. so the equation would be y=1/4x-2
Step-by-step explanation:
suppose that you are awarded prize money if you match at least three of the winning numbers. the probability that you will win some prize money is .
Answers
The frequency of winning numbers you can match, determines your chance of winning a prize.
The likelihood of earning some money is one if you can match three or more of the winning numbers (certain). However, the probability of winning any prizes is zero if you can only match two or fewer of the winning numbers (impossible).
Probability distribution: The probability that a random variable will take on a specific value or range of values is expressed mathematically as a probability distribution. It is often referred to as a probability mass function or a probability density function (PDF) (PMF). Each result of a random event, such as the roll of a dice, the toss of a coin, or a stock market return, is given a probability by the probability distribution.
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Madelyn's office recycled a total of 21 kilograms of paper over 3 weeks. After 4 weeks, how many kilograms of paper will Madelyn's office have recycled? Solve using unit rates.
Answers
The quantity of kilograms of paper that Madelyn's office would have recycled after 4 weeks would be = 28kg
How to calculate the quantity of recycled paper?The recycling activities of Madelyn's office in weeks is listed below:
The total quantity of paper recycled for 3 weeks = 21 kg
Then, after 4 weeks would be = xkg
To calculate the unit rate is to find out the quantity recycled per week;
That is,
3 weeks = 21 kg
1 week = X
Make X the subject of formula;
X = 21/3
X= 7 kg
Then if 7 kg = 1 week
X kg = 4weeks
X kg = 7×4/1
= 28 Kilograms
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you can infer causality from a correlational result, but only when the r value is greater than
a.0
b.0.5
c.1
Answers
A correlational result can be used to infer causality, but only if the value of r is greater than 0.
What is infer causality?In statistics, a correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. A positive correlation coefficient implies that two variables are related (as one variable increases, so does the other), whereas a negative correlation value shows that two variables are inversely related (as one variable increases, the other decreases).A correlation value of zero shows that no relationship exists between two variables. However, a correlation coefficient greater than 0 does not imply causality, meaning that it cannot be concluded that one variable causes changes in the other variable. Establishing causality requires additional evidence and methods such as experimental designs or causal inference techniques.To learn more about infer causality refers to:
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Josiah and Katya are asked to build an accessibility ramp to a building. josiah suggests a triangle with side lengths 6, 8, and 10. katya suggets a triangle with side lengths 4, 9, and 12. which ramp creates a right triangle?
Answers
what is the equation for a line that passes through the point (8,-1) and is parallel to the line that passes through points (-2,2) and (6,6)
Answers
Answer:y=2x-15
Step-by-step explanation:
First, we find the slope of the first line
Slope equation:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Plug-in values
[tex]\frac{6-2}{6-(-2)}[/tex]
=[tex]\frac{4}{8}[/tex]=[tex]\frac{1}{2}[/tex]
Slope=1/2
Remember that parallel lines have the same slope.
Now, we use the slope to get the y-intercept.
We start from (8,-1)
We go up 1 (rise) and right 2 (run), or the opposite of the slope (-1 rise, -2 run).
We get a y-intercept of -5.
Plug into y=mx+b
y=1/2x-5
I need help on this problem
Answers
The distance of Main Street is given by the equation D = 319.25 feet
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the distance of Main Street be D
Now , let the triangle be represented as ΔABC
The base of the triangle BC = 300 feet
The hypotenuse of the triangle AC = distance between First avenue and Canal street
The measure of angle ∠BAC = 70°
From the trigonometric relations , we get
sin θ = opposite / hypotenuse
Substituting the values in the equation , we get
sin 70° = 300 / D
Multiply by D on both sides of the equation , we get
D ( sin 70° ) = 300
Divide by sin 70° on both sides , we get
D = 300 / ( sin 70° )
On further simplification , we get
D = 300 / 0.939692
D = 319.2535
D = 319.25 feet
Hence , the distance is 319.25 feet
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the dotplot above shows the distribution of calf measurements for 507 adults who attend a local gym. the data is divided into equal-sized subgroups with 25% of the adults in each subgroup. which measure of center can you most accurately estimate from this information?
Answers
which measure of center can you most accurately estimate from this information: Median
The median divides the data into equal-sized groups. So approximately 50% of the data is above the median and approximately 50% of the data is below the median.
Calculating the median
The median is the value in a data set, implying that half of data focuses have a value more modest or equivalent to the median and half of data focuses have a value higher or equivalent to the median.
For a little data set, you first count the quantity of data focuses (n) and organize the data focuses in expanding request. Assuming the quantity of data focuses is lopsided, you add 1 to the quantity of places and separation the outcomes by 2 to get the rank of the data point whose value is the median.
The rank is the place of the data point after the data set has been organized in expanding request: the smallest value is rank 1, the second-smallest value is rank 2, and so forth.
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the complete question is:
The dotplot above shows the distribution of calf measurements for 507 adults who attend a local gym. The data is divided into equal-sized subgroups with 25% of the adults in each subgroup.
Which measure of center can you most accurately estimate from this information?
1. mean
2. median
if the variance of the population a is 10 and the variance of the population b is 15, does it mean that population a has less variability than population b?
Answers
Yes, the given statement is true if the variance of the population 'a' is smaller than the variance of population 'b' it represents that population 'b' is more variable than 'a'.
Population variance represents the measurement of spread of group data points.It shows the average squared deviation from the given mean.Whenever data points are very near to the mean then the variance has smaller value.And when data points are far away to the mean then it has larger value of variance.Here variance of population 'a' is 10 which is smaller than the variance of population 'b' .It represents population 'a' is less variable than population 'b'.Therefore, the given statement is true for the variance of population 'a' and 'b'.
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Find the area of this circle. Use 3 for pie
Answers
Answer:
3
Step-by-step explanation:
A = 3 × (1ft)²
A = 3 × 1 ft²
A = 3ft²
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answers
2(x-7) = 36
2x - 14 = 36
(add 14 to both sides)
2x = 50
(divide 2 by both sides)
x = 25
which function models the table? Help!!
Answers
Two boats were 400 miles apart at midnight and were both sailing to the same port on Honolulu. One boat was heading west and the other was heading east. If they both arrived at 8:00am, find the speed of each boat if one was 20MPH faster than the other.
Answers
The speed of the air or water increases and its pressure decreases as it circles the longer-path side of the sail or keel. The air or water will attempt to migrate from the side of high pressure to the side of low pressure as it moves along the sail or keel in response to the consequent pressure difference.
How is sailing speed determined?Theoretical displacement hull speed is determined by the following equation: velocity in knots = 1.35 x waterline length in feet squared.
Use x to symbolise the slower boat's speed.
Therefore, the faster boat's speed would be x + 20 mph.
They met for 8 hours, hence the distance they travelled overall during that period is depicted as
Distance: (x + 20) * 8 + x * 8
Thus, we have
Distance: 16x plus 160
At twilight, the two boats were separated by 400 kilometres.
The distance equation is as follows.
400 = 16x + 160
Analyze similar terms
16x = 240
multiply by 16
x = 15
Remember that
20 mph faster boat equals x.
Thus, we have
Speedier boat = 15 plus 20
Speedier boat = 35
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If I paid $625 interest on $5000 that I borrowed at 5%, how many years did I borrow it? *Remember, I = P x R x T
Answers
Answer:
2½ years
Step-by-step explanation:
I =PxRxT
$625=$5000 x 5/100 x T
$ 625= $250 T
625/250=T
T = 2.5
Solve for x on the diagram below
Answers
Answer:
x = 60°
Step-by-step explanation:
the 'x' angle and the adjacent 120° angle form a straight line
a straight line consists of 180°
the difference of two numbers is 52. the larger number is three less than six times the smaller number. find the numbers. (enter your answers as a comma-separated list.)
Answers
If the difference of two numbers is 52 and larger number is six times the smaller number , then the smaller number is 11 , larger number is 63 .
Let the smaller number be denoted by "x".
according to the information that, "larger number is three less than six times the smaller number" ;
So, the larger number can be represented as 6x - 3.
The difference between the two numbers is 52,
that means ; (6x - 3) - x = 52
On Solving for x ;
we get ;
⇒ 5x = 55
⇒ x = 11
Therefore , the smaller number is 11, and the larger number is 6×11-3 = 63.
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Hexagon HEXAGZ has vertices H(3,0), E(1, -2), X(-1, -2), A(-3,0), G(-2,2), and Z(1,2). What are the coordinates of the image of HEXAGZ for a dilation with center (0,0) and a scale factor of 3.5?
Answers
Answer: ion know
Step-by-step explanation: 1 + 2 = 3
Chad buys a frying pan priced at $26. If the sales tax is 10%, how much tax will Chad pay?
Answers
Answer:
$2.60
Step-by-step explanation:
10% = 0.1
26 times 0.1 = $2.60
So, Chad pays $2.60 tax.
Answer:$28.60-26= 2.60
Step-by-step explanation:
$26 = 100%
sales tax = +10%
total price 26 x 110%
Solve for x :
[tex] \it{ \large{2x - 6 = 2(3x + 5)}}[/tex]
Thank You!
Answers
2x-6x=6+10
-4x=16 (divide both sides with -4)
X=-4
Rule: 1, 2, 3, 5, 8,
Answers
Answer: 13, 21, 34...
Step-by-step explanation: 1+2 = 3, 2+3 = 5, 3+5 = 8, 5+8 = 13, 8=13 = 21, etc.
In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the mass of the substance was 1300 grams and mass was decreasing by 14% per day. Determine the mass of the radioactive sample at the beginning of the 11th day of the experiment.
Answers
Answer:
At the beginning of the 11th day, the mass of the radioactive sample was 201.87 grams.
Step-by-step explanation:
Let's call the mass of the substance after n days "m". We can calculate the mass for each day using the formula:
m = 1300 * (1 - 0.14)^n
Plugging in n = 11:
m = 1300 * (1 - 0.14)^11
m = 1300 * 0.15572634
m = 201.87 grams
So at the beginning of the 11th day, the mass of the radioactive sample was 201.87 grams.
lisle and linda walk in opposite directions from the same point. lisle walks 0.8 kilometers every 10 minutes, and linda walks 2.8 kilometers every 30 minutes. how far apart are they after 1 hour?
Answers
The total distance between lisle and Linda will be 10.4 kilometers.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that lisle and Linda walk in opposite directions from the same point. lisle walks 0.8 kilometers every 10 minutes, and Linda walks 2.8 kilometers every 30 minutes.
lisle's distance in an hour:-
0.8 x 6 = 4.8 Km
Linda's distance in an hour:-
2.8 x 2 = 5.6 Km
Total distance = 4.8 + 5.6 = 10.4 Km
Therefore, there will be 10.4 kilometers between Lisle and Linda overall.
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Question 6 Mathematics
Answers
The predicted number of barrels of crude oil for October is given as follows:
19.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
y = -0.02x² + 0.14x + 19.6.
October is the 10th month, hence the prediction is obtained as follows:
y = -0.02(10)² + 0.14(10) + 19.6
y = 19.
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Pleeeeeeeeeeeaaaaaaaaaaase help me soon
Answers
Answer:
third choice in image. √(16³)
the squareroot of 16 to the third power
Step-by-step explanation:
Fractional exponents tell you that you have roots. Could be squareroot or thirdroot, fourth root, fifth root...etc. You know which because you look at the bottom number (denominator) of the fraction. I use the phrase "down and out" to help remember that the bottom number in the fractional exponent is the "outside number" (index) on the radical sign.
The top number (numerator) of the fraction is an exponent. It can be either inside the radical right there on the shoulder of the 16 or it could also be outside the whole entire radical.
16^ (3/2) = √(16³) = (√16)³
please help i need this asap!
Answers
Answer: Infinitely many solutions
Answer:
Below
Step-by-step explanation:
15x + 3y = 27 divide through by 3 to get
5x + y = 9 <====== this is the same equation as the first one so they are the SAME line ....meaning INFINITE solutions
divide a by 2 in algebraic expression
Answers
Answer: a/2
I believe for this problem all they’re asking is how you would write the expression.
Number 8 please will give brainliest
Answers
Answer: X= 90
Step-by-step explanation:
There is a 90-degree symbol. So I think X= 90.
Thank you
what is the unit of measurement for coding the length of lacerations? a. square inches b. inches c. square centimeters d. centimeters
Answers
The unit of measurement for coding the length of lacerations d)centimeters.
Centimeters are the most common unit of measurement used to code the length of lacerations. This is because they are a small enough unit of measurement that they can accurately describe even the smallest of lacerations.
Centimeters are also the most commonly used metric unit of length, making them the most useful when coding lacerations for medical records. In addition, centimeters are a more precise unit of measurement than inches and are accepted internationally as a unit of measurement, making them the best choice when coding lacerations.
Finally, centimeters are consistent units of measurement, making it easy to compare laceration lengths between different patients and different medical records.
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the average area of a bedroom in a home is 219 square feet with a standard deviation of 32.5 square feet. what is the largest a bedroom can be and be among the smallest 20% of bedrooms in a home?
Answers
The largest a bedroom can be and still be among the smallest 20% of bedrooms in a home is around 271 square feet.
To understand this answer, we have to use the concept of standard deviation, which is a measure of how spread out the data is from the mean. In this case, the average area of a bedroom is 219 square feet, with a standard deviation of 32.5 square feet. To calculate the 20th percentile, we need to find the value of X such that P(X < x) = 0.20, where P(X < x) is the cumulative distribution function of X.
We can use a standard normal table to find the Z-score corresponding to 0.20 and then convert it back to the original scale. The Z-score for 0.20 is -0.84. Therefore, x = 219 + 32.5 * (-0.84) = 271, which is the largest a bedroom can be and still be among the smallest 20% of bedrooms in a home.
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