Can someone please help me with continuity? I would like to check my work, I’m a bit confused on the differentiability part
Answers
For f to be continuous at some point x = c, you require that
• f(c) exists and is finite, and
• the limits of f as x approaches c from either side match, and their value must be f(c)
For f to be differentiable at x = c, you require that
• f is continuous at c (i.e. the above conditions are all met), and
• the derivative f ' is continuous at c
Without having the graph of f ', you can assess whether the last condition is met by some function by mentally tracing a tangent line to the graph as you get closer to c. If the slope of the tangent doesn't change, then the function is differentiable. This is usually accompanied by jumps or sharp corners in the graph.
Some examples:
• every polynomial is both continuous and differentiable
• the absolute value function |x| is continuous but not differentiable at x = 0
• 1/x is neither continuous nor differentiable at x = 0
(a) Neither continuous nor differentiable
Why? f has a vertical asymptote at x = -2 and f (-2) does not exist. f is not continuous, and therefore not differentiable.
(b) Neither continuous nor differentiable
Why? From the left, f is approaching 2.5, while from the right, it's approaching 5.
(c) Neither continuous nor differentiable
Why? The limits from either side of x = 2 match and are equal to 0.5, but f (2) itself does not exist (which is indicated by the point being a hollow circle).
If the circle was instead filled in, so that f (2) = 0.5, then f would be continuous there, but still not differentiable. Notice the sharp corner. Or, using the tangent-line analysis, the slope of the tangent to the left of x = 2 is negative, but to the right it would be positive.
(d) Both continuous and differentiable
Why? f doesn't have any special features at x = 3 that would suggest it's not continuous nor differentiable.
(e) Neither continuous nor differentiable
Why? Similar reasoning as in (a). There's another vertical asymptote, but the graph shows f (4) = 1. However, the limits from either side of x = 4 are positive infinity, not 1.
Related Questions
A hotel manager is adding a tile border around the hotel's rectangular pool. let n represent the width of the pool, in feet. the length is 3 more than 3 times the width, as shown. Write two expressions that represent the perimeter of the pool.
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Answer:
[tex]2(4n+3)[/tex]
[tex]8n+6[/tex]
Step-by-step explanation:
We are given that
Let n represent the width of pool
Length of pool=[tex]3n+3[/tex]
We have to find two expression which represent the perimeter of the pool.
We know that
Perimeter of rectangle=[tex]2(l+b)[/tex]
Where l=Length of rectangle
b=Width of rectangle
Using the formula
Perimeter of pool=[tex]2(n+3n+3)[/tex]
Perimeter of pool=[tex]2(4n+3)[/tex]
Perimeter of pool=[tex]8n+6[/tex]
Hence, two expressions that represent the perimeter of the pool is given by
[tex]2(4n+3)[/tex]
[tex]8n+6[/tex]
Plz help me! I’m not sure how to do these!
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Answer:
Step-by-step explanation:
Wait where is the picture
Convert the point-slope form to slope-intercept form. y - 5 = 3(x - 2)
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Answer:
y = 3x - 1
Step-by-step explanation:
distribute on the right side of equation first
y - 5 = 3x - 6
now add 5 to each side
y = 3x - 1
Answer:
Step-by-step explanation:
y - 5 = 3x - 2
y = 3x + 3
PLEASE SOMEONE HELP THIS IS THE LAST ANSWER ON MY TEST BUT I DONT KNOW MATH GOOD???
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Answer:
x = 7
Step-by-step explanation:
Helppppp!!!!!!!!!!!!
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Answer:
y = 2/3x
Step-by-step explanation:
What is the leading coefficient of the polynomial F(x) defined below?
Answers
Answer: 2
Step-by-step explanation:
The leading coefficient is just the value before the variable with the highest power. So first we must find the portion in your polynomial that has the highest degree. The highest degree simply means the variable with the highest power. The highest power is two, so we will look at the coefficient of that portion. The coefficient of 2x^2 is 2 .
a bacteria culture doubles every 3 minutes. if 400 bacteria started, how long will it take before there are 2000 in the culture?
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Answer:
15 minutes
Step-by-step explanation:
400 to 2000(x5)
so, 3 times 5 is equal to 15 min
True or false ; 3/4 > 0.65
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true
oops, i read it wrong LOL, it's true. .65 is less than .75
Describe the image when a scalene triangle is rotated 180 degrees counterclockwise
about the origin.
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Answer:
It is a same size scalene triangle as the original triangle.
Step-by-step explanation:
:)
Answer: Choice B
It is a same size scalene triangle as the original triangle.
Step-by-step explanation:
A. It is a smaller scalene triangle than the original triangle.
B.(It is a same size scalene triangle as the original triangle.)
C.It is a larger scalene triangle than the original triangle.
Which statement is true regarding the intervals where the function is increasing and decreasing? The function is increasing from (–∞, 0). The function is increasing from (0, ∞). The function is decreasing from (–∞, 0). The function is decreasing from (–∞, ∞).
Answers
Step-by-step explanation:
mark me as a brainlist hope its helpful yo you
The function is increasing from (–∞, 0). Then the correct option is A.
What is increasing and decreasing of function?If the value of y increases as the value of x increases, then increasing function.
And if the value of y decreases as the value of x increases, then decreasing function.
From the graph, the function is increasing from (–∞, 0).
Then the correct option is A.
The complete question is attached below.
More about the increasing and decreasing of function link is given below.
https://brainly.com/question/14330051
#SPJ2
Find the volume of the cylinder and cone, then add them together.
Answers
★ Volume of cylinder :-
V = πr²hHere,
r is radius h is heightWe have :
r = 2cm h = 7cmSubstituting the values :
> V = π (2 × 2) × 7
> V = 4π × 7
> V = 28π
★ Volume of cone :-
V = ⅓ π²hWe have :
r = 2cm h = 6 cmSubstituting the values :
> V = ⅓ × π × (2 × 2) × 6
> V = ⅓ × π × 4 × 6
> V = ⅓ × π × 24
> V = 8π
★ According to the question :-
Adding them together,
> Total Volume = 8π + 28π
> Total Volume = 36π
[tex]Total \: \: \: Volume = (88+176) {cm}^{2} \\ \\ = 264 {cm}^{2} .[/tex]
In order to pay for his expenses, Chuck needs to earn $2400 at least every
month. When Chuck works overtime, he earns $3000 per month. If the
variable e stands for the amount of money Chuck has left after paying for his
expenses every month, which of the following choices is the most reasonable
value for e when he works overtime?
A. $120
B. $1200
C. $600
D. $5400
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Answer:
5400
Step-by-step explanation:
2400+3000
A tree cast a shadow 21 meters long. The angle of elevation of the sun is 51 degrees. What is the height of the tree?
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Answer:
64feet
Step-by-step explanation:
Tim deposit 4500 in a savings account that pays 4.5% simple interest. How much interest does she earn into years?
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Answer:
ummmm is it meant to ask in 2 years instead of into years? if so
Which critical thinking issue is most relevant to the following situation:
A survey asks the following: Should the President have the line item veto to eliminate waste?
self-interest study
O assumed accuracy from overly precise numbers
voluntary response bias
Ononresponse bias or missing data
perceived lack of anonymity
loaded or leading question
Answers
Answer: loaded or leading question
Step-by-step explanation:
Loaded or leading questions aim to elicit a particular response from the respondents by including an assumption that makes people feel bad or good if they answer in a certain way. It essentially plays on their emotions and ideals.
The question in the survey is a loaded question because in saying/assuming that the veto will be able to eliminate waste, it makes people more likely to vote in the affirmative as they would want the president to either get rid of waste or would feel bad if they did vote for such an environmental endeavour.
Verify that f and g are inverses functions using composition , show your steps
Answers
Answer:
See explanations below
Step-by-step explanation:
Given the functions
f(x) = 12x - 12
g(x) = x/12 - 1
To show they are inverses, we, must show that f(g(x)) = g(f(x))
f(g(x)) = f(x/12 - 1)
Replace x with x/12 - 1 into f(x)
f(g(x)) =12((x-12)/12) - 11
f(g(x)) = x-1 - 1
f(g(x)) =x - 2
Similarly for g(f(x))
g(f(x)) = g(12x-12)
g(f(x)) =(12x-12)/12 - 1
12(x-1)/12 - 1
x-1 - 1
x - 2
Since f(g(x)) = g(f(x)) = x -2, hence they are inverses of each other
Maliha thinks of a number x write an expression for the number Maliha gets when she multiples the number by 3
Answers
Answer:
3x
Step-by-step explanation:
Answer:
3x = y
Step-by-step explanation:
MARKING PEOPLE AS BRAINLIST
Which Additional fact would prove that quadrilateral WXYZ is a parallelogram?
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Answer:
A
Step-by-step explanation:
I need help fast I appreciate it
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11.) In the equation 6x = 84, what is the next step in the equation solving sequence?
Isolate the variable through inverse operations.
Solve for the variable.
Identify and move the coefficient or variable.
Combine like terms.
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Answer:
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
-6*x-(84)=0
Step by step solution :
STEP 1: Pulling out like terms
1.1 Pull out like factors :
-6x - 84 = -6 • (x + 14)
Equation at the end of step 1:
STEP 2: Equations which are never true
2.1 Solve : -6 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
2.2 Solve : x+14 = 0
Subtract 14 from both sides of the equation :
x = -14
One solution was found :
x = -14
Answer: i think u should divide 84 by 6 to keep x alone the answer is x=14
but the answer depends on the sign of the variable .
Step-by-step explanation:
what is the slope of (4,8) and (10,7)
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Answer:
The answer is -1 / 6
Step-by-step explanation:
use the formula y2 - y1 / x2 - x1 = m
7 - 8 / 10 - 4 = -1 / 6
A:-1/6
Jim invested $750 in a 3-year CD that earns 4.2% annual interest that is compounded monthly. How much will the CD be
worth at the end of the 3-year term? Include the dollar sign in your answer, and round to the nearest cent.
Provide your answer below:
Answers
Answer:
4.2% of 750 = 31.5
31.5 * 3 = 94.5
~Hope this helps~
The worth of CD after 3 years will be $853.07 at the given rate of interest.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
Given that,
Principle amount P = $750
Rate of interest R = 4.3%
Time period T = 3 years
Number of times interest compounded annually (n) = 12
The compound interest formula is given by;
A = P[1 + R/n]^nT
A = 750[ 1 + 4.3/1200]¹²⁽³⁾
A = $853.07
Hence "The worth of CD after 3 years will be $853.07 at the given rate of interest".
For more information about compound interest,
brainly.com/question/26457073
#SPJ6
If Q is the midpoint between P and R, PQ = 3x + 2 and QR = 7x - 18, find the value of x.
Answers
Answer:
x = 5
Step-by-step explanation:
Since Q is the midpoint of PR,
PQ = QR
=> 3x + 2 = 7x - 18
=> 3x - 7x = -18 - 2
=> -4x = -20
=> x = -20/-4
=> x = 5
Hope it helps :)
Please mark my answer as the brainliest
please help me . i'm trying to get my grades up and i'm struggling
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Answer:
D
Step-by-step explanation:
just took that test
Analyze the diagram below and complete the instructions to follow.
Find a, b and c
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Answer/Step-by-step explanation:
✔️Using trigonometric ratio, find b:
Reference angle = 45
opposite = 8
Hypotenuse = b
Thus,
Sin(45) = 8/b
b = 8/sin(45)
b = 8/(1/√2) (sin 45 = 1/√2)
b = 8 × √2/1
b = 8√2
✔️Find a using trigonometric ratio:
Reference angle = 60°
Hypotenuse = b = 8√2
Adjacent = a
Therefore,
Cos(60) = a/8√2
8√2*cos(60) = a
8√2*½ = a
4√2 = a
a = 4√2
✔️Find c using Pythagorean Theorem:
c² = b² - a²
c² = (8√2)² - (4√2)²
c² = 128 - 32
c² = 96
c = √96
c = √(16*6)
c = 4√6
What is the product?
213 × 314
Answers
Answer:
66882
Step-by-step explanation:
Answer:
product
Step-by-step explanation:
213×314=66,882
Which function shows a positive rate of change?
Answers
Answer: C
Step-by-step explanation:
C. because rate of change is the slope aka y/x. The other answers give off negative slopes when determining y/x.
The total number of points scored during 10 regional games is shown below.
52, 51, 65, 38, 56, 48, 50, 31, 46, 31
Select the correct five-number summary for this data set. (4 points)
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Answer:
Min 31
Q1 38
Median 49
Q3 52
Max 65
Step-by-step explanation:
Max number
Min number
Answer:
Min: 31
Q1: 38
Median: 49
Q3: 52
Max: 65
Step-by-step explanation:
Min Number: 31
Max Number: 65
Laura invests $2,000 in a bank account which pays a compound interest rate of 6.4%. To the nearest cent, what amount is in the account after 5 years and what amount of interest earned over 10 years?
Answers
Answer:
9,000
Step-by-step explanation:
it you count with time by ×it would be 9,000 because just add that up with money
MARKING BRAINLIEST
Which sentence is an example of an objective summary from Cynthia Crossen's "A Culinary Wasteland"?
A. Furthermore, Mr. Schlosser's appraisal is not comprehensive but a hodgepodge of impressions, statistics, anecdotes and prejudices.
B. As a stickler about statistics, I was disturbed by Mr. Schlosser's cavalier manipulation of data, which produced some startling — and, frankly, unbelievable — "facts."
C. Americans are addicted to cheap, bad food, he argues, and like all addictions, this one exacts broad and often unseen costs from the community.
D. Taking individual responsibility for one's impact on the global economy is far more complicated than just saying no to fast food, as Mr. Schlosser advises.