Mathematics High School

Consider the following limit of Riemann sums of a function f on [a,b]. Identify f and express the limit as a definite integral. lim Δ→0
​
∑ k=1
n
​
x k
∗
​
tan 2
x k
∗
​
Δx k
​
;[1,2] The limit, expressed as a definite integral, is (Simplify your answers.)

Answers

Answer 1

To identify the function f and express the given limit as a definite integral, we can observe the Riemann sum expression and recognize its similarity to the definition of the definite integral. Answer : ∫[1,2] x * tan^2(x) dx.

In the given expression, we have the Riemann sum:

∑ k=1^n x_k * tan^2(x_k) * Δx_k

To express this limit as a definite integral, we recognize that the function f(x) = x * tan^2(x) is being approximated by the Riemann sum.

We can rewrite the Riemann sum as:

∑ k=1^n f(x_k) * Δx_k

Now, we can see that the function f(x) = x * tan^2(x) and the interval [a, b] are given. In this case, a = 1 and b = 2.

To express the given limit as a definite integral, we take the limit as Δx_k approaches zero and rewrite the Riemann sum as the definite integral:

lim Δx_k→0 ∑ k=1^n f(x_k) * Δx_k

This limit can be written as:

∫[a,b] f(x) dx

Substituting the values of a and b, we have:

∫[1,2] x * tan^2(x) dx

Therefore, the limit expressed as a definite integral is ∫[1,2] x * tan^2(x) dx.

Learn more about  Riemann sum: brainly.com/question/30404402

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Related Questions

Find the surface area of the
triangular prism.
10 ft.
3 ft.
3 ft

Answers

Given:

The figure of a triangular prism.

To find:

The surface area of the triangular prism.

Solution:

We know that, a triangular prism contains 2 congruent triangular surface and 3 rectangular surface.

Triangles have base 3 ft and height 2 ft.

Area of a triangle is

[tex]Area=\dfrac{1}{2}\times base\times height[/tex]

[tex]A_1=\dfrac{1}{2}\times (3)\times (2)[/tex]

[tex]A_1=3[/tex]

Area of congruent triangles are congruent. So,

[tex]A_1=A_2=3\text{ sq. units}[/tex]

Now the three rectangular surface have dimensions 10 by 3, 10 by 3 and 10 by 3 because the triangles are equilateral and the length of the prism is 10 ft.

Area of a rectangle is

[tex]Area=Length\times width[/tex]

[tex]A_3=10\times 3[/tex]

[tex]A_3=30[/tex]

Dimensions of all three rectangles are same, therefore there areas are equal.

[tex]A_3=A_4=A_5=30[/tex]

Now, the total surface area of the prism is

[tex]A=A_1+A_2+A_3+A_4+A_5[/tex]

[tex]A=3+3+30+30+30[/tex]

[tex]A=96[/tex]

Therefore, the total surface area of the prism is 96 sq. ft.

plz I need help on this really bad :(

Answers

Answer:

x+3y=4x+y

Step-by-step explanation:

filipino.munting gamogamo.malaking gamugamo​

Answers

Answer:

i Don't understand what ur saying

Step-by-step explanation:

Answer:

Nagtatanong ka ba? kung ganun ano yun

You deposit $1,600 in a bank account. The account pays 3% annual Interest compounded monthly. Find the balance after 5 years

Answers

Step-by-step explanation:

step 1. let's call the amount of money A, the initial amount P, the yearly rate r, the number of compounds per year n.

step 2. A = P(1 + r/n)^(nt)

step 3. A = 1600(1 + .03/12)^((12)(5)

step 4. A = 1600(1.0025)^(60)

step 5. A = $1858.59

Order the angles in each triangle from smallest to largest.

Answers

the answer is D

an easy way to think about it is considering the missing side from the measures given
for example LN = 17, the missing side is M so we know that the measure of angle M is 17, which is the smallest
for MN = 21, the missing side is L so the second smallest is angle L

8r2 in fraction form

Answers

8r^2 eight r squared hope this is right

It is the simplest fraction form

Maria ha invitado a 18 de sus compañeros de clase a su fiesta de cumpleaños .Si en total tiene 30 compañeros ,¿que porcentaje de la clase ha ido a su fiesta?

Answers

Answer:

59.9%

Step-by-step explanation:

100/30 = 3.3

3.3*18 = 59.9%

What is the next term of the geometric sequence?
20, -10,5,

Answers

Answer:

0

Step-by-step explanation:

Answer: -2.5

Step-by-step explanation:

-3/4x=-5

Please help fast!!!

Answers

Answer:

x=3.75

Step-by-step explanation:

-3/4x=-5

x-3    x-3

4x=15

/4   /4

x=3.75

Answer:

x = 3.75

Step-by-step explanation:

-3/4x = -5

(-3/4) -3/4x = -5(-3/4)

x = 3.75

¿Sera cierto que existe una fraccion con numerador 20 equivalente a la fraccion 100/55?Justifica tu respuesta​

Answers

Answer:

si porq si porq si si dices si es si

5/2k+1=-9
What does k equal?

Answers

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

If you mean,

[tex] \frac{5}{2k} + 1 = - 9[/tex]

Then the answer would be,

[tex]k = - \frac{1}{4} [/tex]

But, if you mean

[tex] \frac{5}{2} k + 1 = - 9[/tex]

Then the answer would be,

[tex]k = - 4[/tex]

Factor the following expression completely.

2x^2y-18y

Answers

Answer:

Since both terms are perfect squares, factor using the difference of squares formula,

a2-b2=(a+b)(a−b) where a=x and b=3.2y(x+3)(x−3)

Step-by-step explanation:

hope this helps!!!

The candy store has a stock of candy. They have 15 bags of tootsie rolls, 10 boxes of nerds, 12 bags of gummy
bears, 5 bags of M&M's and 22 bags of skittles. Find the ratio of tootsie rolls to total candy in the store. Be sure
to simplify

Answers

Answer:

15:49

Step-by-step explanation:

15 : 10+12+5+22

15 : 49

Can't be simplified further.

15:49 because it cannot be simplified

Find the length of y

Answers

Answer:

25 cm

Step-by-step explanation:

Tyler has $415 in his savings Tyler has $415 in his savings account account. He earns $45 a week mowing lawns. Write and solve an equation.using b for the variable to find how many weeks will he to work to have $1315 saved?

Answers

Answer:

20 weeks

Step-by-step explanation:

1315$-415$=900$

900/45=20

Hence 20 weeks

Answer: 45b  

Step-by-step explanation: Divide 1315 with 45xb.

What is the difference from congruent figures and similar figures

Answers

Answer:

similar = only the angles are the same

congruent = angles and sides are the same

Only the angles are the same

What multiplication fact could help me find out 24 ÷ 8 ?

Answers

Answer:

Step-by-step explanation:

That would be 8 x 3. It would help because 24/8 = 3.

If we divide 24 by 8 it gives us the result of 3.

So a multiplication fact is 8x3 = 24.

Please help:
Find the class width of this graph

Answers

Answer:

The biggest one is 32 to 38

Step-by-step explanation:

hope it helps

-2x + 4 = -3x + 4
3
One Solution
No Solution
Infinite Solutions

Answers

Answer:

X=0 or no solution

Step-by-step explanation:

-2x+4=-3x+4

cancel equal terms on both sides of the equation

-2x=-3x

move the variable to the left-hand side and change its sign

-2x+3x=0

collect like terms

x=0

please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! will give brainliest!!!!!!

Answers

Answer:

X is 40

Step-by-step explanation:

Look it up

X=40 will be the answer

What is the volume of this?

Answers

Answer:

270 m³

Step-by-step explanation:

[tex]A_{triandle}[/tex] = [tex]\frac{5*12}{2}[/tex] = 30 m²

[tex]V_{triangular prism}[/tex] = 30 × 9 = 270 m³

There are 9 counters in a bag.

7 of the counters are green.
2 of the counters are blue.

Ria takes at random two counters from the bag.

Work out the probability that Ria takes one counter of each colour.

Answers

The Answer:
7:2
Hope this helps

how to the medium in the dot line????!! I don't want my mom to be mad at my grade please!!!!!!

Thank you whoever helps me!

Answers

Answer: To find the median, count the dots from left to right until you find the middle value.

Step-by-step explanation:

Ok so first it's not a dot line it's a dot plot. Second, let's define what a medium is. The medium is the "middle" of a sorted list of numbers. To find the Median, place the numbers in value order and find the middle number. Example: find the Median of {13, 23, 11, 16, 15, 10, 26}. The middle number is 15, so the median is 15. Tip to find the median from a list of value ordered numbers every time cross a number from each side. For example, if you cross 13 from above also cross 26 and if you cross 23 then also cross 10.

Back to your original question of how to find the medium on a dot plot you need to take all the numbers from your dotted line put them in order even if they are repeated and then cross each one on each side from right to left. Also remember if you cross out all the numbers right and left and end up with two numbers left then take them and add them and then divide by 2 and that will be the median.

An example is attached on here in order to help you understand what I am saying. Hope this helps. Your welcome and I hope you make your mama proud.  

Your class earned $120.00 Saturday afternoon by washing cars to raise money for the class trip. This is 1/4 of the money needed for the trip. What is the total amount needed?

Answers

Answer:

$360.00

(I hope this was helpful)

A medical provider is doing a study to determine the average time spent waiting before an appointment. The current average wait time is 34 minutes, which is 15% shorter than the average was when the study started. What was the average wait time then?

Answers

Answer:

39.1 minutes

Step-by-step explanation:

Given that:

Current wait time = 34 minutes

Current wait time is 15% shorter than average wait time when study started.

Average wait time when study started :

15% of current wait time :

0.15 * 34

= 5.1 minutes

Average wait time when study started :

34 minutes + 5.1 minutes

= 39.1 minutes

a²-a² what is the answer​

Answers

Answer:

a² - a² = 0

hope it helps

Answer:

a ² - a ²= 1 a ² - 1 a ² = 0

you understand ?

Tell weather each pair is parallel, perpendicular, or neither: y= 3x + 2 2y= 6x -6

Answers

The pair are parallel to eachother. The second equation in slope intercept form is y = 3x-3, since they have the same slope they’re parallel.
They are parallel!
When you put 2y=6x-6 into slope intercept form, you get y=3x-3.
They are parallel because they have the same slope.
Perpendicular lines have opposite reciprocal slope. For example, one equation would have a slope of 3 and the second one would have a slope of -1/3.
Hope that makes things more understandable!

Perry's bikes rent bikes for $18 plus $4 per hour. Lea paid $42 to rent a bike for how many hours did she rent the bike?

Answers

Answer:

10.5 hours!

Step-by-step explanation:

she rented the bike for 6 hours

In the figure shown the sum of the measures yxz and wxv is 75 degrees . what is the measure of zxw​

Answers

Answer: 105 = WXZ

Step-by-step explanation:

180 = WXZ + 75

subtract both sides by 75 and you get WXZ is equal to 105

I'm not 100% sure, lmk if I'm wrong

Was wondering if anyone knows the answer to part A and B for this question?

Answers

Answer:

no idea

Step-by-step explanation:

Answer:

k so from my opinion

I think the answer is gonna be a

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