For numbers 1 to 5, evaluate the limits. (4 points each) 1 lim 4-x2 X2 X2-2x 2. lim sin O sin 5x lim X xer
Answers
The limit of (4-x^2)/(x^2-2x) as x approaches 0 is 3. The limit of sin(θ)/sin(5θ) as θ approaches 0 is 1/5. The limit of x / (x + e^x) as x approaches to limit 1. The limit of [(x - 2) / sqrt(x - 1) - sqrt(3)] as x approaches infinity is 0. The limit of [(1 + 2x)^5 - 1] / x as x approaches to limit is 10.
We are given the limit:
lim x → 2 [(4 - x²) / (x² - 2x)]
We can factor the numerator and denominator
lim x → 2 [(2 + x)(2 - x) / x(x - 2)]
The term (x - 2) in the denominator cancels with the same term in the numerator, leaving
lim x → 2 [(2 + x) / x] = 2 + 2/2 = 3
Therefore, the limit is 3.
We are given the limit
lim x → 0 (sin(x) / sin(5x))
Using L'Hopital's rule, we can take the derivative of the numerator and denominator with respect to x
lim x → 0 (cos(x) / (5cos(5x)))
Substituting x = 0, we get
lim x → 0 (cos(x) / (5cos(5x))) = cos(0) / (5cos(0)) = 1/5
Therefore, the limit is 1/5.
We are given the limit
lim x → ∞ x / (x + e^x)
We can divide both the numerator and denominator by x:
lim x → ∞ (1 / (1 + e^(-x)))
As x approaches infinity, e^(-x) approaches zero, so we can simplify the expression to:
lim x → ∞ (1 / 1) = 1
Therefore, the limit is 1.
We are given the limit:
lim x → 2 [(x - 2) / sqrt(x - 1) - sqrt(3)]
We can simplify the expression by multiplying the numerator and denominator by the conjugate of the first term in the numerator
lim x → 2 [(x - 2) / sqrt(x - 1) - sqrt(3)] * [(sqrt(x - 1) + sqrt(3)) / (sqrt(x - 1) + sqrt(3))]
Expanding the numerator and simplifying, we get
lim x → 2 [(x - 2)(sqrt(x - 1) + sqrt(3)) / (x - 1 - 3)] = lim x → 2 [(x - 2)(sqrt(x - 1) + sqrt(3)) / (x - 4)]
Substituting x = 2, we get
lim x → 2 [(x - 2)(sqrt(x - 1) + sqrt(3)) / (x - 4)] = 0
Therefore, the limit is 0.
We are given the limit:
lim x → 0 [(1 + 2x)^5 - 1] / x
We can use the binomial theorem to expand the numerator:
(1 + 2x)^5 = 1 + 5(2x) + 10(2x)^2 + 10(2x)^3 + 5(2x)^4 + (2x)^5
Substituting this into the limit expression and simplifying, we get:
lim x → 0 [(1 + 2x)^5 - 1] / x = lim x → 0 [(5(2x) + 10(2x)^2 + 10(2x)^3 + 5(2x)^4 + (2x)^5) / x]
= lim x → 0 (10 + 40x + 80x^2 + 80x^3 + 32x^4) = 10
Therefore, the limit is 10.
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--The given question is incomplete, the complete question is given
" For numbers 1 to 5, evaluate the limits. (4 points each)
lim x → 2 [(4 - x²) / (x² - 2x)]
lim x → 0 (sin(x) / sin(5x))
lim x → ∞ x / (x + e^x)
lim x → 2 [(x - 2) / sqrt(x - 1) - sqrt(3)]
lim x → 0 [(1 + 2x)^5 - 1] / x "--
Related Questions
bob and rob in ratio 3:4 and their age 4 years ago was 5:7 find their ages
please answer (asap)
thnx pls do in one variable
Answers
Answer:
Present Day:
Bob:Rob:Difference
3 : 4 : 1
6 : 12 : 2
4 years ago:
Bob:Rob:Difference
5 : 7 : 2
The equation of the function shown can be written as
y = a(x-blank 1)(x-blank 2)(x-blank 3)
Blank 1:
Blank 2:
Blank 3:
Answers
Answer:
\(y=a(x-(-1))(x-2)(x-6)\)
First blank -1
Second blank +2
Third blank +6
Step-by-step explanation:
The x-intercepts of the graph are its zero's so if we see the graph it cuts the x-axis at 3 points -1 , +2 and +6 so the factors would be
\(f(x)=a(x+1)(x-2)(x-6)\)
The equation is always written as factors of the equation in terms of where the polynomial intersects the x-axis.
Kamal and Anand each Lent the same sum of money for 2 years at 5 percent at simple interest and compound interest respectively. Anand received RS.15 more than Kamal.Find the amount of money lent by each and interest received
Answers
Answer:
amount lent: ₹6000interest received: Kamal, ₹600; Anand, ₹615.Step-by-step explanation:
For principal P invested at simple interest rate r, the returned value in t years is ...
A = P(1 +rt)
If K is Kamal's returned value, the given numbers tell us ...
K = P(1 +0.05·2) = 1.1P
__
For principal P invested at compound interest rate r, with interest compounded annually for t years, the returned value is ...
A = P(1 +r)^t
If A is Anand's returned value, the given numbers tell us ...
A = P(1.05)² = 1.1025P
This latter amount is RS.15 more than the former one, so we have ...
1.1025P = 1.1P +15
0.0025P = 15 . . . . . . . . subtract 1.1P
P = 6000 . . . . . . . . . . . divide by 0.0025 . . . . the amount lent
Kamal received 1.1P -P = 0.1P = 600 on the investment.
Each lent ₹6000. Kamal received ₹600 in interest; Anand received ₹615 in interest.
I found this answer on the Internet. *If* it were an original answer, below is how I would grade it and why.
The Chord Intersection Theorem:
If 2 chords of a circle are AB and CD and they intersect at E, then
AE * EB - CE * ED.
Problem.
Two Chords AB and CD intersect at E. If AE = 2cm, EB = 4 and CE = 2.5 cm, find the length of ED.
By the above theorem: 2*4= 2.5 * ED
ED = (2 * 4)/2.5
3.2 cm.
Answers
Answer:
1) It is given that line AB is tangent to the circle at A.
∴ ∠CAB = 90º (Tangent at any point of a circle is perpendicular to the radius throught the point of contact)
Thus, the measure of ∠CAB is 90º.
Why is it difficult to identify the slope of the line `6x-2y=12`?
Answers
Answer:
Prolly cause it's not in slope intercept form.
Step-by-step explanation:
To make the equation into slope-intercept form, first subtract 6x from both sides.
-2y = -6x + 12
Divide everything by -2.
y = 3x - 6
There is your slope-intercept equation. -6 is the y-intercept and 3 is the positive slope.
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Find the sum of the primes between 100 and 200, inclusive, that are 1 or 2 more than a perfect square.
Answers
Answer:
298
Step-by-step explanation:
All perfect squares from 100-200 inclusive:
100, 121, 144, 169, 196
100+1=101, 101 is prime
121+2=123, 123=41*3 so its not prime
144+1=145 145=29*5 so its not prime
169+2=171 171=9*19 so its not prime
196+1=197, 197 is prime
101+197=298
Notice that I excluded all even numbers because they are obviously composite.
One year consumers spent an average of $22 on a meal at a restaurant. Assume that the amount spent on a restaurant meal is normally distributed and that the standard deviation is $6. What is the probability that a randomly selected person spent more than $23?
Answers
The probability that a randomly selected person spent more than $23 is approximately 0.4332 or 43.32%.
To find the probability that a randomly selected person spent more than $23, we need to use the standard normal distribution formula:
Z = (X - μ) / σ
where X is the amount spent on a restaurant meal, μ is the mean amount spent, σ is the standard deviation, and Z is the corresponding standard normal random variable.
Substituting the given values, we have:
Z = (23 - 22) / 6
Z = 0.1667
Using a standard normal distribution table or calculator, we can find the probability that Z is greater than 0.1667, which is:
P(Z > 0.1667) = 0.4332
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A man on a 135 ft verticals cliff looks down at an angle of 16 degrees and sees his friend. How far away is the man from his friend? How far is the friend from the base of the cliff?
Answers
Answer:
a) 489.77 ft from friend
b) 470.80 ft from cliff
Step-by-step explanation:
Given a man on a 135 ft cliff sees his friend at an angle of depression of 16°, you want to know the distance of the man from his friend, and the distance of the friend from the cliff.
Trig relationsThe relevant trig relations are ...
Sin = Opposite/Hypotenuse
Tan = Opposite/Adjacent
GeometryThe 135 ft height of the cliff is modeled as the side of a right triangle that is opposite the angle of elevation from the friend to the top of the cliff. (See attachment 2.) That angle is the same as the angle of depression from the top of the cliff to the friend.
The hypotenuse of the triangle is the distance between the man and his friend. The side of the triangle adjacent to the friend is the distance to the cliff.
Using the above relations, we have ...
sin(16°) = (cliff height)/(distance to friend)
tan(16°) = (cliff height)/(distance to cliff)
Solving for the variables of interest gives ...
distance to friend = (cliff height)/sin(16°) = (135 ft)/sin(16°) ≈ 489.77 ft
distance to cliff = (cliff height)/tan(16°) = (135 ft)/tan(16°) ≈ 470.80 ft
The ma is 489.77 ft from his friend; the friend is 470.80 ft from the cliff.
__
Additional comment
The distances are given to more decimal places than necessary so you can round the answer as may be required.
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Arianna correctly simplified an expression. When she substituted mc020-1. Jpg into the simplified expression, the value was â€"4. Which could be Arianna’s original expression? One-sixth (negative 3 x minus 24) One-sixth (negative 5 x minus 8) One-sixth (negative 10 x minus 4) One-sixth (negative 12 x minus 16).
Answers
Answer:
value was â€"4. Which could be Arianna’s original expression? One-sixth (negative 3 x minus 24) One-sixth (negative 5 x minus 8) One-sixth (negative 10 x minus 4) One-sixth (negative 12 x minus 16).
Answer:
C.)1/6 (-10x-4)
Step-by-step explanation:
Got it right on edge 2022
Aimee and Desmond are going to a play this evening.
Desmond wants to have at least $50 in his wallet. He
currently has $5. Write and solve an inequality to find
how much more cash Desmond should put in his wallet.
Answers
Answer:
45
Step-by-step explanation:
x+5 =50
x=45
What output corresponds with I2?
Answers
Answer:
Solve for the input that corresponds to the given output value. (Round answers to three decimal places when appropriate. Enter your answers as a comma-separated list. Note: Even though the question may be completed without the use of technology, the authors intend for you to complete the activity using the technology you will be using.
Step-by-step explanation:
what is the square root of 5 times 3 divided by 2 to the power of 10
Answers
Answer:
0.0065509804
Step-by-step explanation:
Answer:
If you follow the order of operations it would be 0.12103072956 or approximately
0.12
0.121
0.1210
0.12103
0.121031
-4x + 64 < 242 + 3x
Giving extra points
Answers
Answer:
x>−178/7
Step-by-step explanation:
I'm assuming you wanted to solve for the inequality of x, if so this is the answer.
In the year 2000, a company made $2.2 million in profit. for each consecutive year
after that, their profit increased by 13%. how much would the company's profit be in
the year 2003, to the nearest tenth of a million dollars?
Answers
The company's profit in the year 2003 is $3.1 million
Profit is defined as the amount of revenue generated after deduction of all the liabilities.
Given that in the year 2000 profit = $2.2 million
Each year increase in profit = 13% =0.13
Total number of year = 2003-2000=3 years
Profit is denoted by
\(profit=initial profit(1+each.year.increase)^{years}\)
Substituting the values we get
profit=\(2.2(1+0.13)^3\)
=\(2.2(1.13)^3=2.2*1.442897\)
=3.174373
=3.1 million
Therefor , the company's profit in the year 2003 is $3.1 million
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Which expressions are in their simplest form? Check all that apply.
Answers
Answer:
The first one is the only one in simplest form.
Answer: this is answerrrr
A C Dpeace
What is (-5) the 2 is an exponent just so you know
Answers
Answer:
25
Step-by-step explanation:
(-5)^2
(-5)*(-5)
25
Answer:
25
Step-by-step explanation:
(-5)^2 = 25, since -5 x -5 is 25.
Now, if the -5 hadn't been in parenthesis, -5^2 would be read as -(5 x 5), and would equal -25.
Brainliest, please! I'm so close to becoming an Expert!
Which statement is true regarding the sides of a triangle
Answers
i don't understand how to answer the question with the denominators value
Answers
When solving a problem involving fractions, it's important to understand the meaning of the numerator and denominator. The numerator represents the part of the whole that we are interested in, while the denominator represents the total number of equal parts that the whole is divided into.
Let's say we have a fraction 2/5. The denominator 5 indicates that the whole is divided into 5 equal parts, while the numerator 2 indicates that we are interested in 2 of those parts.
Therefore, the fraction 2/5 represents the ratio of 2 out of 5 equal parts of the whole.To answer a question involving fractions with a denominator of 200, you need to know that the whole is divided into 200 equal parts.
Then you can use the numerator to represent the specific part of the whole that is being referred to in the question.For example, let's say a question asks what is 1/4 of the whole when the denominator is 200.
We know that the whole is divided into 200 equal parts, so we can set up a proportion:1/4 = x/200To solve for x, we can cross-multiply:
4x = 1 x 2004x = 200x = 50
Therefore, 1/4 of the whole when the denominator is 200 is 50. In this way, you can approach any question involving fractions with a denominator of 200 or any other number by understanding the meaning of the numerator and denominator and setting up a proportion.
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Factor the following polynomial completely.
A.
B.
C.
D.
Answers
Step-by-step explanation:
Please write complete question
Answer:
lol u gotta put the thing first bro
Step-by-step explanation:
A bird flies 8.64 meters above the pond. A fish swims below the bird at -1.78 meters from the surface of the water. How many meters apart are the bird and the fish?
Answers
Does 5p + 11 represents "5 times the sum of p and 11?" How do you know (explain your reasoning).
Answers
Answer:
No
Step-by-step explanation:
It does not because 5 times the sum of p and 11 is written like this :-
5(p + 11)5p + 55So, it's not the same.
To get 5p + 11, the correct statement should be :-
11 more than than the product of p and 5An arithmetic sequence has common difference d. the series sums s2, s5 and s7 themselves form an arithmetic sequence. find, in terms of d, the common difference for this sequence.
Answers
To find the common difference for the arithmetic sequence formed by the series sums s2, s5, and s7, let's analyze the given information.
The sum of the second term (s2), fifth term (s5), and seventh term (s7) themselves form an arithmetic sequence.
Let's denote the second term as a + 2d, the fifth term as a + 5d, and the seventh term as a + 7d, where 'a' is the first term and 'd' is the common difference.
Using the arithmetic sequence formula for the sum of terms, we have:
s2 = (2/2) * (2a + (2-1)d) = 2a + d
s5 = (5/2) * (2a + (5-1)d) = 5a + 6d
s7 = (7/2) * (2a + (7-1)d) = 7a + 12d
Since the sums s2, s5, and s7 themselves form an arithmetic sequence, we can express their differences:
s5 - s2 = (5a + 6d) - (2a + d) = 3a + 5d
s7 - s5 = (7a + 12d) - (5a + 6d) = 2a + 6d
Now, equating the differences, we have:
3a + 5d = 2a + 6d
Simplifying the equation, we find:
a = d
Therefore, the common difference for the arithmetic sequence formed by the series sums s2, s5, and s7 is 'd'.
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Given two events, a and b, with probabilities p(a) = 0.40 and p(b) = 0.20, calculate the indicated probabilities given the additional piece of information
Answers
Answer:
0.60
Step-by-step explanation:
becouse of two probability within added gives the above answer
Geometry help please !!! I need this for extra credit in school
Answers
Answer:
I believe it is y = -3x + 2
Step-by-step explanation:
Mia is saving up to buy a new video game. She has $10 saved so far, and she can save $2 from her allowance each week. How long will it take her to save up the $28 she needs? write an equation and solve.
Answers
i need help!!!! list the factors of -108 that equal to -3
Answers
Answer:
9 and -12
Step-by-step explanation:
Whoever gets this correct gets brain, 5 stars and a thanks! An explanation of it would be amazing! Tysm!
Answers
Answer:
D: 12
Step-by-step explanation:
1) So what I did at first was convert the fractions into decimals.
(Personally, this makes it easier, for me at least)
\(\frac{1}{4} = 0.25\\\)\(\frac{3}{5} = 0.60\)2) The problem states that for every 0.25 cups of broccoli, 0.60 grams of fiber are added as well to the mix. You can also convert this into a fraction. (It doesn't matter which one is the numerator/denominator, but for this example, I used the 0.25 cups of broccoli as the numerator.
\(\frac{broccoli}{fiber} =\frac{0.25}{0.60}\)3) Next step would be making another fraction. This time, the fraction is for the 5 cups of broccoli. Since we don't know the amount of grams for the fiber, we will replace it with an "x".
\(\frac{broccoli}{fiber} =\frac{5}{x}\)4) Realize, that | \(\frac{0.25}{0.60} =\frac{5}{x}\) | To figure out the answer to this part, you can cross-multiply
\(0.25x = 5(0.60)\)\(0.25x = 3\)5) Then at last, divide both sides by \(0.25\) and you'll get:
\(x=12\)Sorry this may have taken a long time; I just wanted to make sure everything was correct. Hope you do well on math, whether it's a test, or just homework. Good luck! :D
A friend gives you two baseball cards for your birthday. Afterward, you begin collecting them. You buy the same number of cards once each week. The equation y = 4x + 2 describes the number of cards, y, you have after x weeks.
Discuss which points on the line do not make sense in this situation. Then plot three more points on the line that do make sense.
Answers
Answer:You have 2 cards upfront, so the constant term in this linear equation is 2. The slope represents how many more cards you buy or acquire per day, week or month (depending upon how eager you are to fatten your collection). ;)
y = 2 + (rate of acquisition of cards)(time)
y = 2 + rt
The product of two numbers is 176 difference is 48
Answers
If orange paint i made with 3 quart of red paint and 2 quart of yellow paint, then how many quart of yellow paint hould be mixed with 6 quart of red paint?
Answers
In linear equation, The quarts of yellow paint mixed with 6 quarts of red paint should be, 4.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.the number of quarts of yellow paint should be mixed with 6 quarts of red paint.
According to question
As, 3 quarts of red paint is mixed with 2 quarts of yellow paint
So, 6 quarts of red paint is mixed with
6/3 * 2 = 4 quarts of yellow paint
Thus, the quarts of yellow paint mixed with 6 quarts of red paint should be, 4.
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