1.Lim as x approaches 0 (sin3x)/(2x-Sinx)
2. Lim as x approaches infinity x^-1 lnx
3. Lim x approaches infinity x/ e^x
Using L’Hospals rule for all
Answers
1. The limit of (sin3x)/(2x - sinx) as x approaches 0 is -27.
2. The limit of x^(-1)lnx as x approaches infinity is -1.
3. The limit of x/e^x as x approaches infinity is 0.
1. To find the limit of (sin3x)/(2x - sinx) as x approaches 0 using L'Hôpital's rule, we can differentiate the numerator and denominator separately and take the limit again:
Let's differentiate the numerator and denominator:
Numerator: d/dx (sin3x) = 3cos3x
Denominator: d/dx (2x - sinx) = 2 - cosx
Now, we can find the limit of the differentiated function as x approaches 0:
lim x->0 (3cos3x)/(2 - cosx)
Again, differentiating the numerator and denominator:
Numerator: d/dx (3cos3x) = -9sin3x
Denominator: d/dx (2 - cosx) = sinx
Taking the limit as x approaches 0:
lim x->0 (-9sin3x)/(sinx)
Now, substituting x = 0 into the function gives:
(-9sin0)/(sin0) = 0/0
Since we obtained an indeterminate form of 0/0, we can apply L'Hôpital's rule again.
Differentiating the numerator and denominator:
Numerator: d/dx (-9sin3x) = -27cos3x
Denominator: d/dx (sinx) = cosx
Taking the limit as x approaches 0:
lim x->0 (-27cos3x)/(cosx)
Now, substituting x = 0 into the function gives:
(-27cos0)/(cos0) = -27/1 = -27
Therefore, the limit of (sin3x)/(2x - sinx) as x approaches 0 is -27.
2. To find the limit of x^(-1)lnx as x approaches infinity using L'Hôpital's rule, we can differentiate the numerator and denominator separately and take the limit again:
Let's differentiate the numerator and denominator:
Numerator: d/dx (lnx) = 1/x
Denominator: d/dx (x^(-1)) = -x^(-2) = -1/x^2
Now, we can find the limit of the differentiated function as x approaches infinity:
lim x->∞ (1/x)/(-1/x^2)
Simplifying the expression:
lim x->∞ -x/x = -1
Therefore, the limit of x^(-1)lnx as x approaches infinity is -1.
3. To find the limit of x/e^x as x approaches infinity using L'Hôpital's rule, we can differentiate the numerator and denominator separately and take the limit again:
Let's differentiate the numerator and denominator:
Numerator: d/dx (x) = 1
Denominator: d/dx (e^x) = e^x
Now, we can find the limit of the differentiated function as x approaches infinity:
lim x->∞ (1)/(e^x)
Since the exponential function e^x grows much faster than any polynomial function, the denominator goes to infinity much faster than the numerator. Therefore, the limit of (1)/(e^x) as x approaches infinity is 0.
Thus, the limit of x/e^x as x approaches infinity is 0.
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Related Questions
X^2+_x+36
What is the Perfect Square Trinomials?
Answers
Answer:
Step-by-step explanation:
hello,
\(36=6*6=6^2\)
and
\((x+6)^2=x^2+12x+36\)
so the missing term is 12 to get a perfect square trinomial
hope this helps
Answer: The answer is "12".
Step-by-step explanation: Correct on edgen. (2022)
Which of the following describes the graph of y = RootIndex 3 StartRoot 8 x minus 64 EndRoot minus 5 compared to the parent cube root function?
stretched by a factor of 2 and translated 64 units right and 5 units down
stretched by a factor of 8 and translated 8 units right and 5 units down
stretched by a factor of 2 and translated 8 units right and 5 units down
stretched by a factor of 8 and translated 64 units right and 5 units down
Answers
Answer:
(c) stretched by a factor of 2 and translated 8 units right and 5 units down
Step-by-step explanation:
The transformed function can be written as ...
y = ∛(8x -64) -5 . . . . . . given
y = ∛(8(x -8)) -5
y = 2∛(x -8) -5
Where f(x) = ∛x, this is of the form ...
y = 2f(x-8) -5
These numbers in these places correspond to ...
vertical stretch by a factor of 2translation 8 units righttranslation 5 units down
Answer:
c
Step-by-step explanation:
18% of what number is 22?
Answers
Answer:122.222222
Step-by-step explanation: hope this helps
can i have brainliest?
The distance between two distinct points: ordered pair 1 (x , y) and ordered pair 2 (x, y) is given by the formula ____?____.(I need the formula)
Answers
Given an ordered pair 1:
\(\mleft(x,y\mright)\)And a distinct ordered pair 2:
\((x,y)\)You can rewrite them as:
\(\begin{gathered} (x_1,y_1) \\ \\ (x_2,y_2) \end{gathered}\)According to the Pythagorean Theorem, for Right Triangles:
\(c=\sqrt[]{a^2+b^2}\)Where "c" is the hypotenuse and "a" and "b" are the legs of the Right Triangle.
Then, you can set up that:
Then, to find the hypotenuse of the Right Triangle or the distance "d" between the points, you can apply the Pythagorean Theorem and set up that:
\(d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\)Therefore, the answer is:
\(d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\)
Solve the equation for x do not include "x=" in your answer -2+/3x-2=6
Answers
Answer:
x=1=2y
Step-by-step explanation:
Cole and his sister took part in a canned food drive. Cole brought in 21 cans of food. His sister brought in 7 fewer cans than he did. Together, how many cans did they bring in?
Answers
If Cole brought 21 cans and his sister brought 7 cans less, then the total number of cans brought by them is 35 cans.
The number of cans which Cole brought = 21 cans of food.
His sister brought in 7 fewer cans than he did, which means she brought in:
⇒ 21 - 7 = 14 cans of food,
Let the total number of food-cans be = "f",
So, the equation to find the number of cans is written as :
⇒ x = 21 + 14,
On adding the number of cans,
We get,
⇒x = 21 + 14 = 35,
Therefore, together they brought in 35 cans of food.
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M = I1+I₂ 31 +32 2 Now let's substitute in our given values. (-2 , 2) = ((-5 Find 2 and y2 We will now set up two equations to solve for our two unknowns of x2 and y₂. (-5 X2 (-5+₂) -5+22), (7+)) 2 - +₂)/2 = We will first want to multiply by 2 on both sides and will get −5+₂= -4 Adding 5 to both sides we get = 7 This is the coordinate of point B. Now we will set up the equation to solve for y2 +y2)/2 =
Answers
The coordinates of point B are (-3, 17).
The given equation is M = I₁ + I₂ = 31 + 32.
Now let's substitute in our given values:
(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)
We will now set up two equations to solve for our two unknowns, x₂ and y₂:
Equation 1: (-5 + x₂) / 2 = -4
Multiply both sides by 2:
-5 + x₂ = -8
Add 5 to both sides:
x₂ = -3
This gives us the x-coordinate of point B.
Equation 2: (-5 + 2 + y₂) / 2 = 7
Simplify:
(-3 + y₂) / 2 = 7
Multiply both sides by 2:
-3 + y₂ = 14
Add 3 to both sides:
y₂ = 17
This gives us the y-coordinate of point B.
Therefore, the coordinates of point B are (-3, 17).
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if a number is an integer, then it is odd
Answers
Answer:
The integers are, -4, -3, -2, -1, 0, 1, 2, 3, 4, ... -- all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero). For example, -5 is an integer but not a whole number or a natural number. An odd number is an integer when divided by two, either leaves a remainder or the result is a fraction. One is the first odd positive number but it does not leave a remainder 1. Some examples of odd numbers are 1, 3, 5, 7, 9, and 11. ... Since odd numbers are integers, negative numbers can be odd.
What is 1 + 1 im stuck on it and i cant figure it out.
Answers
its 2...
20 leterssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
A rectangular prism has a length of 2 centimeters, a height of 8 centimeters, and a
width of 13 centimeters. What is its volume, in cubic centimeters?
Answers
The volume of the rectangular prism is 208cm³
What is the volume of a rectangular prism?Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Sometimes, volume is also termed capacity.
The volume of a rectangular a prism is expressed as base area × height. The base area is a rectangle and the area of a rectangle is Length × width
length = 2cm
width = 13 cm
height = 8cm
base area = 13× 2 = 26cm²
Volume of the prism = 26× 8 = 208cm³
Therefore the volume of the rectangular prism is 208cm³.
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How would one convert 6 lb to ounces (16 oz = 1 lb)?
O A. 6 lb
16 oz
1 lb
O B.
6 lb
16 OZ
O C. 6 lb x 16 oz
O D. 61bx
1 lb
16 oz
Answers
Answer:
6 * 16
Step-by-step explanation:
One pound is 16oz.
Multiply the number of pounds by 16.
6 * 16 = 96
6 pounds is 96oz.
Hope this helps.
Answer:6lb x 16oz/1lb
Step-by-step explanation:just took the test
Liam has $62. He saves an equal amount of money each week for 6 weeks. Now he has $110. How much money did Liam save each week?
Answers
Answer:
Step-by-step explanation:
Liam saved $8 each week for 6 weeks.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Let's represent the amount of money Liam saves each week as x.
According to the problem, Liam saves an equal amount of money each week for 6 weeks, so the total amount he saves is 6x.
If we add this to the amount he started with, we get the total amount he has now: 6x + 62.
We also know that he now has $110, so we can set up an equation:
6x + 62 = 110
Subtracting 62 from both sides gives:
6x = 48
Dividing both sides by 6 gives:
x = 8
Therefore,
Liam saved $8 each week for 6 weeks.
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Differentiate. y = (x2 - 2x + 6) ex O (2x - 2) et O (x2 + 4x + 4) et 0 (x² + 4) ex 03 + 4x + 6 ex 3 400
Answers
Differentiate y
so,
\(\begin{gathered} y^{\prime}=(2x-2)\cdot e^x+(x^2-2x+6)\cdot e^x \\ y^{\prime}=(2x-2+x^2-2x+6)\cdot e^x \\ y^{\prime}=(x^2+4)\cdot e^x \end{gathered}\)so, the answer is option 3
=======================================================
Note: we have used the rule of y = f(x) * g(x)
y' = f'(x) * g(x) + f(x) * g'(x)
A caterer charges a $40 fee plus an additional $6.25 per person. She determines the total cost, C, for x people by using the equation shown above. How much will a party cost for 80 people?
Answers
$40+$6.25(80)=c
What is the slope intercept form. slope of 0 and passes through (1,3)
Answers
Answer:
Step-by-step explanation:
y - 3 = 0(x - 1)
y - 3 = 0
y = 3
Michelle can swim 4 laps in 6 minutes and 12 seconds. If michelle swims at the same pace, how long would it take her to swim 10 laps?
Answers
Answer:
9 laps takes 5 minutes 25 seconds.
Step-by-step explanation:
Here is given:
4 laps takes 6 minutes 12 seconds.
We have to find how long 1 lap takes.
4/4 6/4 12/4 --> 1 lap takes 2 minutes 33 seconds.
Now, multiply each by 9 because you want to find 9 laps, so:
1x9 2x9 33x9 --> 9 laps takes 5 minutes 25 seconds.
Hope this helps :)
It would take Michelle 15 minutes and 50 seconds to swim 10 laps
In which number is the digit 4 ten times larger than in the number 384?
O 842
O 954
O 1,469
O 4,216
Answers
The number 842 is the number whose digit 4 is ten times larger than in the number 384
Finding the numberTo solve the problem, we need to find a number in which the digit 4 is ten times larger than in the number 384.
In the number 384, the digit 4 is in the ones place, which means that its value is 4.
To find a number in which the digit 4 is ten times larger, we need to find a number in which the digit 4 is in the tens place and its value is 10 times larger than 4, which is 40.
The only answer option that fits this description is 842. In this number, the digit 4 is in the tens place and its value is 40, which is ten times larger than its value in the number 384.
Therefore, the correct answer is 842.
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2x - 7 + 3x = 4x + 2 need help with this one
Answers
Answer:
x = 9
Step-by-step explanation:
To solve the equation 2x - 7 + 3x = 4x + 2 for x, you can follow these steps:
Combine like terms on both sides of the equation. Add the x terms together and move the constant terms to one side of the equation:
2x + 3x - 4x = 2 + 7
Simplifying the left side: x = 9
Simplify the right side of the equation:
x = 9
Therefore, the solution to the equation is x = 9.
0.50416667 rounded to the nearest hundredth
Answers
At Barbra Books, each customer that spends at least $10 gets to draw a coupon from a bag that contains $1 coupons and $5 coupons. After the coupon is drawn, the savings is applied to the customer's purchase, and then the coupon is replaced in the bag.
The number of $1 coupons and $5 coupons drawn Monday through Friday last week is recorded in the double bar graph below.
Based on the information in the graph, what is the experimental probability that a $5 coupon is the next coupon drawn?
A. 97/167
B. 70/167
C. 95/167
D. 72/167
Answers
Answer:
To find the experimental probability that a $5 coupon is the next coupon drawn, we need to add up the total number of $5 coupons drawn and divide it by the total number of coupons drawn.
Looking at the double bar graph, we can see that a total of 272 coupons were drawn from Monday to Friday, and out of those, 173 were $5 coupons. Therefore, the experimental probability of drawing a $5 coupon is:
Experimental probability = Number of $5 coupons drawn / Total number of coupons drawn
Experimental probability = 173 / 272
Simplifying this fraction by dividing both the numerator and denominator by 17, we get:
Experimental probability = 10 / 16
Converting this fraction to a decimal, we get:
Experimental probability = 0.625
Therefore, the experimental probability of drawing a $5 coupon is 0.625 or 625/1000.
However, none of the answer choices matches this value. The closest one is 70/167, which is approximately 0.419 (rounded to three decimal places). This value does not match the experimental probability calculated above. So, there may be an error in the question or answer choices.
Answer:
There is error in question or answer choices.
Convert the height of a person who is 5.2 feet tall to centimeters. Include the inches-centimeter conversion
factor. Use the table given to create conversion factors. Show all conversion factors needed.
Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional
analysis that you learned.
Answers
The height of the 5.2 feet person in centimeters is 158.496 cm.
Explain unit conversion.A conversion factor must be added, subtracted, multiplied, or divided throughout the multi-step process of unit conversion. Additionally, selecting the appropriate number of significant digits and rounding may be necessary.
Different conversion units are used to quantify various measurements. By definition, unit conversion is the process of converting two measures of the same quantity between distinct units by multiplying or dividing them.
In mathematics, conversion is the process of changing a value's form, such as from millimeters to inches or liters to gallons. Units are used for measurements of length, weight, capacity, temperature, and speed.
Given,
Height of a person = 5.2 feet.
The conversion between inches and centimeters must also be included.
First, convert feet to inches.
1 foot = 12 inches
Converting the given height to inches,
Height = 5.2 × 12
= 62.4 inches
Now, we will convert the height into centimeters,
To convert, we will multiply by 2.54
Height = 62.4 × 2.54
= 158.496 cm
Therefore, the height of the person in centimeters is 158.496 cm
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Ramesh dan syarika ans. Ramesh takes a medical and health insurance policy with a deductible of RM1 500 per year and co-insurance of 20% of covered medical expenses. Ramesh went to the hospital for the first time for knee treatment and the medical cost was RM700, the medical cost for the second and third treatments was RM2 000 and RM1 700 respectively. The three treatments were in the same year. How much medical expenses should be borne by Ramesh and the insurance company?
Answers
Ramesh will bear a total medical expense of RM1,760, and the insurance company will cover RM2,900.
1. Ramesh's deductible is RM1,500 per year. This means that he is responsible for paying the first RM1,500 of medical expenses before the insurance coverage kicks in.
2. For the first treatment, the medical cost was RM700. Since this amount is less than the deductible, Ramesh will have to pay the entire RM700 out of pocket.
3. For the second treatment, the medical cost was RM2,000. Since Ramesh has already met his deductible with the first treatment, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the remaining RM500 (RM2,000 - RM1,500), which amounts to RM100. The insurance company will cover the remaining 80% of RM500, which amounts to RM400.
4. For the third treatment, the medical cost was RM1,700. Again, since Ramesh has already met his deductible, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the entire cost, which amounts to RM340 (20% of RM1,700). The insurance company will cover the remaining 80% of RM1,700, which amounts to RM1,360.
5. To calculate the total medical expenses borne by Ramesh, we add up the amounts he is responsible for in each treatment: RM700 + RM100 + RM340 = RM1,140.
6. The total medical expenses covered by the insurance company can be calculated by adding up the amounts they pay in each treatment: RM400 + RM1,360 = RM1,760.
7. Finally, to find the overall amount borne by Ramesh and the insurance company, we sum up the individual expenses: Ramesh's expenses + insurance company's expenses = RM1,140 + RM1,760 = RM2,900.
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Solve the system of equations y= x squared + 3x-6 and y=2x-6
Answers
Answer:
Slope = 4.000/2.000 = 2.000
x-intercept = 6/2 = 3
y-intercept = -6/1 = -6.00000
Step-by-step explanation:
Step by step solution :
Step 1 : Equation of a Straight Line
Graph of a Straight Line
Calculate the Y-Intercept
Calculate the X-Intercept
Calculate the Slope
Answer for y=2x-6 is below
Answer:
Slope = 4.000/2.000 = 2.000
x-intercept = 6/2 = 3
y-intercept = -6/1 = -6.00000
Hope this helps.
What attributes were used to organize the shapes in Circle A and Circle B?
Circle A Circle B
Attribute of Circle A:
Attribute of Circle B:
Help me please I am not that go in math
Answers
Answer: attribute of circle A
Step-by-step explanation: took it ur good
Celeste is planting a rectangular flower garden in which the width will be 4 feet less than its length. She has decided to put a birdbath within the garden that will occupy a space 3feet by 4 feet how many feet are now left for planting? Express your answer on factored form
Answers
Answer:
(L-6)(L+2)
Step-by-step explanation:
Let L be the length of the flower garden.
Then the width will be L-4.
The area of the flower garden = L*(L-4) =L²-4L
The area of the birdbath is 3*4 = 12 ft²
The area of the remaining space for planting is
= Area of flower garden - area of birdbath
L² - 4L - 12We can factor the expression as follows:
L² - 4L - 12 L²-(6-2)L-12L²-6x+2x-12taking common frome each two terms
L(L-6)+2(L-6)(L-6)(L+2)Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.
Abby is filling a 100 quart dog bath using a 2 gallon bucket. how many buckets will it take to fill the dog bath?
Answers
( or 12.5 buckets)
Step by step
We know the bath holds 100 quarts
We know 100 quarts is equal to 25 gallons
( 4qts to 1 gallon)
If Abby is using a 2 gallon bucket, divide 25 gallons by 2
25/2 = 12 1/2 buckets to fill the bath
The factor tree below provides the factors of 18.
18
N.
2
9
3
3
What is the prime factorization of 18?
2 x 3
2 x 9
2 x 3x3
02x3x9
Answers
Answer: it is (c)
i hope this helped :)
7st + 4t(s + t + 4) - 9t
Answers
Answer:
11ts + 4t^2 + 7t
Step-by-step explanation:
7st + 4t(s + t + 4) - 9t
= 7st + 4ts + 4t^2 + 16t - 9t
= 11ts + 4t^2 + 7t
Answer: 11st + 4t² + 7t
Step-by-step explanation:
Expand 4t(s + t + 4) into: 4st + 4t² + 16t
7st +4st + 4t² +16t - 9t
Add and subtract to get your answer
Help please!!!!! THIS IS URGENT
Answers
Answer:
There will be $22,800 left after 6 years
Step-by-step explanation:
4% every year after 6 years = 24% be taken out of 30,000
24% of 30,000 = 7200 so you'll have 22,800 left.
Answer:
I beleve the answer is $22,600 after 6 years
Step-by-step explanation:
-3= 6 +?
Help ASAP!!
Answers
Answer:
-9
Step-by-step explanation:
-3 = 6 - 9
-3 = -3