Answers
Answer:
[tex]\lim_{x \to 5}f(x)=-5\\\lim_{x \to 1^-} f(x)=3\\\lim_{x \to 1^+} f(x)=3\\\lim_{x \to 1} f(x)=4\\[/tex]
Step-by-step explanation:
[tex]\lim_{x \to 5}f(x)[/tex]
This means "the limit of f(x) as x approaches 5"
In this case, f(x) is a basic linear function while x > 1, so a limit is not necessary but it can still be used as it is here. For this one, you can just calculate f(5), and that is:
[tex]f(x)=5-2x[/tex]
[tex]f(5)=5-2(5)=5-10=-5[/tex]
[tex]\lim_{x \to 5}f(x)=-5[/tex]
===================
[tex]\lim_{x \to 1^-} f(x)[/tex]
This one is a little different. It means "the limit of f(x) as x approaches 1 from the negative (left) direction"
The negative direction of course means x will be less than 1, so we'll use this function:
[tex]f(x)=4-x[/tex]
It's easier if you graph it, but you can also do it like this:
[tex]f(0)=4+0=4\\f(0.5)=4-0.5=3.5\\f(0.75)=4-0.75=3.25\\f(0.9)=4-0.9=3.1\\f(0.99)=4-0.99=3.01[/tex]
There's a clear pattern there. You can see that f(1) should be 3, but this function only applies while x is less than 1 so it can never reach 3. It will get infinitely close, and that can be shown with the limit:
[tex]\lim_{x \to 1^-} f(x)=3[/tex]
===================
[tex]\lim_{x \to 1^+} f(x)[/tex]
This one works the same way, but from the positive (right) direction.
[tex]f(2)=5-4=1\\f(1.5)=5-3=2\\f(1.25)=5-2.5=2.5\\f(1.1)=5-2.2=2.8\\f(1.01)=5-2.02=2.98\\f(1.001)=5-2.002=2.998[/tex]
It will also get infinitely close to 3 when x = 1, but won't ever reach it because this function only applies when x is greater than 1.
[tex]\lim_{x \to 1^+} f(x)=3[/tex]
===================
[tex]\lim_{x \to 1} f(x)[/tex]
Here, the function for x=1 is just:
[tex]f(x)=4[/tex]
It's given already, so the limit is just:
[tex]\lim_{x \to 1} f(x)=4[/tex]
Related Questions
HELP ME OUT PLEASE
Use the data to create a scatter plot.
Answers
Find the measure of angle
Answers
9514 1404 393
Answer:
(b) 62°
Step-by-step explanation:
Let x represent the measure of the angle.
The complement is (90 -x).
The supplement is (180 -x).
The relationship between the supplement and the complement is ...
(180 -x) = 6 +4(90 -x)
180 -x = 6 +360 -4x
3x = 186
x = 62
The measure of the angle is 62°.
Is (2, 1) a solution to the equation y = 2x - 1?
Answers
Answer:
No
Step-by-step explanation:
Substitute the values for their respective variable and evaluate.
[tex]1=2(2)-1\\1=4-1\\1\neq 3[/tex]
Therefore, (2, 1) is not a solution to the equation y = 2x - 1.
(2, 1) is in the form of (x, y).
Then,
☆ x = 2
☆ y = 1
Equation =》y = 2x - 1
Now, substitute the values.....
=》y = 2x - 1
=》(1) = 2(2) - 1
=》1 = 4 - 1
=》 1 ≠ 3
So, (2, 1) is NOT a solution to the equation y = 2x - 1.
______
Hope it helps ⚜
-0.15 as a mixed number
Answers
Answer:
A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number. It is partly a whole number. It is partly a fraction.
Please Help! I don't understand how the Alabama paradox works. I will give you a lot of points!
--PLEASE show all work
The table shows the populations, in thousands, of the three states in a country with a population of 3760 thousand. Use Hamilton's method to show that the Alabama paradox occurs if the number of seats in congress is increased from 24 to 25
Answers
Answer:
State A loses a seat to State B when the total is increased
Step-by-step explanation:
The "work" is most easily done by a spreadsheet, as the calculations are easily defined and very repetitive.
The "fair share" of seats is the fraction the population is of the total, multiplied by the total number of seats. It will generally be a mixed number (integer plus fraction).
If the whole number is 1 or greater, the number of seats allocated at least that whole number.
If not all seats are allocated, the fractions are sorted in decreasing order, and 1 additional seat is added to the allocation for each state, working down the list, until all of the seats are allocated.
__
The attachment shows State A has the highest fraction when the number of seats is 24. Only one additional seat needs to be allocated in that case. State A gets that extra seat.
When the number of seats is 25, States B and C have the highest fractions. Each of them gets one additional seat, and State A gets no additional seats. This results in the appearance of State A giving up a seat to State B.
_____
Additional comment
Hamilton's apportionment method was used for a number of years in the US. The method now in use is substantially different. The current method would divide the 24 seats so that A=3, B=6, C=15. The 25th seat would be given to State A.
X to the third power equals 512
Answers
Answer:
8
Step-by-step explanation:
translate the graph of f(x) ___ 3 units
the point ___ is on the graph of g(x)
Answers
Answer:
Down 3 unitsStep-by-step explanation:
Given functions:
f(x) = ∛x and g(x) = ∛x - 3The g(x) is a translation of f(x) down 3 units, as g(x) = f(x) + b is a vertical shift b units (up if b > 0, down if b < 0)
The second part of question is unclear as drop down is not visible to us
4 friends share 5 pizzas equally how much pizza did each friend get
Answers
Answer:
10
Step-by-step explanation:
deoends how many pieces each pizza has. if it has 8 pieces each it would be 8×5=40
Find the equation of the line with slope m = 2 that contains the point (8,19).
Answers
Answer:
y = 2x + 1
Step-by-step explanation:
Pls mark as brainliest
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The equation of the line with slope m = 2 and point (8, 19) is
y = 2x + 3
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Slope:
m = 2
Point = (8, 19) = (x, y) _____(A)
Now,
The equation of a line is given as,
y = mx + c ______(B)
Substitute (A) into (B)
From (A) we get,
19 = 2 x 8 + c
19 = 16 + c
c = 19 - 16
c = 3
Now,
The equation of the line with slope m = 2 and point (8, 19) is
y = 2x + 3
Thus,
The equation of the line with slope m = 2 and point (8, 19) is
y = 2x + 3
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ2
2. (a) Use a prove by contradiction to show that if a and b are nonzero integers such that a divides b and a + b is odd, then a is odd. (b) Prove that if n is a positive integer, then n² does not equal 2(mod 4).
Answers
a. Assume a is even, so a = 2k for some integer k. Now let a and b be integers such that a divides b and a + b is odd.
Since a divides b, b = an for integer n, and in turn b = 2nk, which means b is even and hence a + b is also even. But this contradicts our initial assumption, so a must be odd.
b. Let n be even, so that n = 2k for some integer k. Then
n² = (2k)² = 4k²
so that n² ≡ 0 (mod 4).
Now let n be odd, so n = 2k + 1 for integer k. Then
n² = (2k + 1)² = 4k² + 4k + 1
so that n² ≡ 1 (mod 4).
Therefore n² is never congruent to 2 (mod 4).
What is the volume, in cubic inches, of a rectangular prism with a height of 7 inches, a width of 10 inches, and a length of 9 inches?
Answers
Answer:
Step-by-step explanation:
87
Answer:
630 in.³
Step-by-step explanation:
To find the volume of a rectangular prism, you can multiply the height, times the width, times the length. So, let's go ahead and do that with the values of the given prism.
7 × 10 × 9 = 70 × 9 = 630
So, our volume is 630...but not so fast. We also have to put in our units. Our units are inches × inches × inches, or inches³. So our final value is 630 in.³
Hopefully that's helpful! :)
can someone help me with this please?
Answers
Answer:
Okay, Please copy paste the question. I cannot see.
Step-by-step explanation:
Jorge wants to find the height of the house, help him find it.
Answers
last one i’m almost done.
Answers
Answer:
AFC
Step-by-step explanation:
You can tell by the angles
Please help do this
Answers
Answer:
1)m+5q=1+5x5 =262)(y-x^3)=3-1^3 =3-1 =23)q(p+2)=3(3+2) =3(5) =154)y+y-x=5+5-6 =10-6 =45)(z+y)÷6=6+6÷6 =26)h(j-h)=3(6-3) = 3x3=97)x+y+y = 5+2+2=98)z^2-y =9-4=59)b(4+a)=2(4+6) =2x10 =2010)m-n+m =5-1+5 = 4+5 =911)(h+j)÷6 = (2+4)÷6 = 1mark as brainliast plz5 divided by 325 what is the strategy to this question and answer
Answers
Answer: 65
Step-by-step explanation: divided the 2
Graph one function of y=1/3tan(x-π)
Answers
Answer:
ayúdame a encontrarla soy de Perú por favor ayuda
2y = 8x- 70
What’s the slope and y intercept?
Answers
(0,-35)
Answer:
slope = 4, y- intercept = - 35
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
2y = 8x - 70 ( divide through by 2 )
y = 4x - 35 ← in slope- intercept form
with slope m = 4 and y- intercept c = - 35
6. Elena writes the equation 6x + 2y = 12. Write a new equation that has:
a. exactly one solution in common with Elena's equation
b. no solutions in common with Elena's equation
c. infinitely many solutions in common with Elena's equation
Answers
Answer:
2x ×2y=15. then solve for equation x and y
Would anyone help me with this please, worth 20 pts.
Answers
Answer:
Below in bold.
Step-by-step explanation:
The perimeter = length of 3 sides of the square + 1/2 the circumference of the circle. The radius of the circle = 2.5 in and its circumference = 2π r and 1/2 of this is π r.
So the perimeter = 3*5 + π r
= 15 + 2.5π
= 22.85 in to the nearest hundredth.
What is the probability that client A, the newborn you’re considering for a 30-year policy, lives to be 30 years old? Client A is a non-Hispanic white male, so look in table 14.
Answers
Using the probability concept, it is found that there is a 0.97555 = 97.555% probability that client A lives to be 30 years old.
A probability is the number of desired outcomes divided by the number of total outcomes, that is:
[tex]p = \frac{D}{T}[/tex]
In this problem:
Out of 100,000 clients, 97,555 lives to age 30, hence [tex]D = 97555, T = 100000[/tex]Then:
[tex]p = \frac{D}{T} = \frac{97555}{100000} = 0.97555[/tex]
There is a 0.97555 = 97.555% probability that client A lives to be 30 years old.
A similar problem is given at https://brainly.com/question/25790531
Answer: The answer is 0.97424
Step-by-step explanation: The other answer... the math is correct, its just that they have read the source table incorrectly.
Age
29-30 = 97,555
30-31 = 97,424
The correct row is 30-31.
97,424 / 100,000 = 0.97424
You can tell this is the case because look at row 0-1.. its a 100% chance of survival. If you read that row as a '1 year old' then 100% of all people survive until they turn 1? Alas, no, this is not true :(
These signs give information about two different towns.
Study these signs carefully. Then, answer the questions and complete the statements
about them below.
Use the drop-down menus to complete each statement.
Answers
Answer:
In which town does the total number have meaning?
Answer: Town B
For Town A, it does not, cannot, does not.
For Town B, does, can, does.
What is the answer to this question: 8V+3=105
Note: this is Vertical/Adjacent/Complementary Angles (Algebraic)
Answers
8V+3=105
clt
8v=105-3
=102
divide both sides by 8v
8v=102/8v
V=12.75
Start with x and cube it
Answers
Answer:
x to the power of 3
Step-by-step explanation:
Find the measure of
Answers
Answer:
64
Step-by-step explanation:
360-115-129=116 (the sum of exterior angles of triangle is 360)
180-116=64
Prices are going up in the ratio 6:5 Write a 60% decrease as a ratio.
HELP PLSSSSSSSSSSSSSSSSSSSSS
Answers
Answer:
To Decrease an amount in a given Ratio, we need to multiply by a fraction that is less than one. For example, in scaling down a recipe for four people into a recipe for 3 people, we would use the ratio of 3 : 4 which means we would multiply all our recipe amounts.
Solve for x given that
4x + 2
7
Answers
Answer:
x = - 1/2 or -0.5
Step-by-step explanation:
Steps on the pic above
what is 4 1/6÷5 please help
Answers
Answer:
It is 5/6
Step-by-step explanation:
For questions like these use caculator soup you can use it for fractions and much more it shows u how to work the problem out also.
Consider the steps to solve the equation.
2
5
(
1
2
y + 20 ) −
4
5
=
9
20
(2y − 1)
Distribute:
1
5
y + 8 −
4
5
=
9
10
y −
9
20
What is the next step after using the distributive property?
A. Use the multiplication property of equality to isolate the variable term on one side of the equation.
B. Use the multiplication property of equality to isolate the constant on one side of the equation.
C. Combine the like terms on the right side of the equation.
D. Combine the like terms on the left side of the equation.
Answers
Answer:
The answer is D
Step-by-step explanation:
D
PLEASE HELP I HAVE 3 MINUTES LEFT TO DO THIS TY
Which expression is equivalent to 5(8 + 9)?
O 40 + 45
O 13 + 9
O 13 + 14
O 40 + 9
Answers
Answer:
40+45
Step-by-step explanation:
17x5 is 85
Answer:
40 + 45
Step-by-step explanation:
5(8 + 9)
= 5*8 + 5*9
= 40 + 45