School started at 8:05 a.m. and ended at 2:40 p.m. The work below shows Erica’s calculation of the length of the school day.

express the limit as a definite integral on the given interval. lim n → [infinity] n ∑ i = 1 cos x i x i δ x , [ 2 π , 4 π ]

Lemur [1.5K]

The limit as a definite integral on the interval $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π , 4π] is $\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$ .

<h3>What is meant by definite integral?</h3>

A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.

Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.

If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.

Let the equation be

$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$

substitute the values in the above equation, we get

= $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π, 4π],

simplifying the above equation

$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$

To learn more about definite integral refer to:

brainly.com/question/24353968

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8 0

1 year ago

How to find MP when discount percent and SP are given

nadezda [96]

Given:

Consider the discount percent and SP are given.

To find:

The MP.

Solution:

Let x% be the discount percent Then

$SP=MP-x\%\text{ of }MP$

$SP=MP-\dfrac{x}{100}MP$

$SP=\left(1-\dfrac{x}{100}\right)MP$

$SP=\left(\dfrac{100-x}{100}\right)MP$

Multiply both sides by 100.

$100SP=(100-x)MP$

Divide both sides by $(100-x)$ .

$\dfrac{100}{100-x}SP=MP$

Therefore, the formula for MP is $MP=\dfrac{100}{100-x}SP$ , where x is the discount percentage.

7 0

2 years ago

Is the binomial a factor of the polynomial nominal function?

Sedbober [7]

The factors for given equation f(x)= $x^{3} +3x^{2} -25x-75$ .

(x-1) - No
(x-3) - No
(x+3) - Yes
(x-5) - Yes
(x+5) - Yes

<u>Step-by-step explanation:</u>

The given equation is f(x)= $x^{3} +3x^{2} -25x-75$ .

Add 0 at the end of the equation.

$x^{3} +3x^{2} -25x-75$ = 0.

Let us group the given equation,

$(x^{3} +3x^{2}) -(25x-75)$ =0.

⇒ Group 1: $x^{3} +3x^{2}$ .

Group 2: $- 25x +75$ .

Pull out factor from each group,

⇒ Group 1: $(x+3)(x^{2})$ .

Group 2: (x+3) (-25).

Join the two group since both (x+3) is common in both groups.

$(x+3)(x^{2} -25)$ =0.

One of the factor is (x+3).

Other factors are solved by the formula, $a^{2}-b^{2} = (a+b) (a-b)$ .

$(x+3)(x^{2} -25)$ = (x+5) (x-5) .

The other factors are (x+5) and (x-5).

7 0

3 years ago

Solve: -(6x+ 8) = 4(17 - x) *

Vlad1618 [11]

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

x = − 38

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The midpoint of (3 x, -2) and (-4, 5y) is (1,4). find x, -y

Mariana [72]

Answer:

(x,-y): (2,-2)

Step-by-step explanation:

M=(x+x)/2,(y+y)/2

Given (1,4)=

$\frac{3x - 4}{2}$

This implies:

$1 = \frac{3x - 4}{2}$

$3x - 4 = 2 \\ 3x = 2 + 4 \\ \frac{3x }{3} = \frac{6}{3} \\ x = 2$

In a similar way,

$4 = \frac{ - 2 + 5y}{2} \\ - 2 + 5y = 8 \\ 5y = 10 \\ y = 2$

The question demanded (x,-y)

Hence(2,-2) is the answer

7 0

2 years ago