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2 years ago

What is unsustainable commercial

Mathematics

1 answer:

lozanna [386]2 years ago

3 0

Unsustainable commercial is not fair for you

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Calculus 2

FinnZ [79.3K]

Answer:

See Below.

Step-by-step explanation:

We want to estimate the definite integral:

$\displaystyle \int_1^47\sqrt{\ln(x)}\, dx$

Using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with six equal subdivisions.

The trapezoidal rule is given by:

$\displaystyle \int_{a}^bf(x)\, dx\approx\frac{\Delta x}{2}\Big(f(x_0)+2f(x_1)+...+2f(x_{n-1})+f(x_n)\Big)$

Our limits of integration are from x = 1 to x = 4. With six equal subdivisions, each subdivision will measure:

$\displaystyle \Delta x=\frac{4-1}{6}=\frac{1}{2}$

Therefore, the trapezoidal approximation is:

$\displaystyle =\frac{1/2}{2}\Big(f(1)+2f(1.5)+2f(2)+2f(2.5)+2f(3)+2f(3.5)+2f(4)\Big)$

Evaluate:

$\displaystyle =\frac{1}{4}(7)(\sqrt{\ln(1)}+2\sqrt{\ln(1.5)}+...+2\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx18.139337$

The midpoint rule is given by:

$\displaystyle \int_a^bf(x)\, dx\approx\sum_{i=1}^nf\Big(\frac{x_{i-1}+x_i}{2}\Big)\Delta x$

Thus:

$\displaystyle =\frac{1}{2}\Big(f\Big(\frac{1+1.5}{2}\Big)+f\Big(\frac{1.5+2}{2}\Big)+...+f\Big(\frac{3+3.5}{2}\Big)+f\Big(\frac{3.5+4}{2}\Big)\Big)$

Simplify:

$\displaystyle =\frac{1}{2}(7)\Big(f(1.25)+f(1.75)+...+f(3.25)+f(3.75)\Big)\\\\ =\frac{1}{2}(7) (\sqrt{\ln(1.25)}+\sqrt{\ln(1.75)}+...+\sqrt{\ln(3.25)}+\sqrt{\ln(3.75)})\\\\\approx 18.767319$

Simpson's Rule is given by:

$\displaystyle \int_a^b f(x)\, dx\approx\frac{\Delta x}{3}\Big(f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...+4f(x_{n-1})+f(x_n)\Big)$

So:

$\displaystyle =\frac{1/2}{3}\Big((f(1)+4f(1.5)+2f(2)+4f(2.5)+...+4f(3.5)+f(4)\Big)$

Simplify:

$\displaystyle =\frac{1}{6}(7)(\sqrt{\ln(1)}+4\sqrt{\ln(1.5)}+2\sqrt{\ln(2)}+4\sqrt{\ln(2.5)}+...+4\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx 18.423834$

6 0

3 years ago

5 times 3/4 in a mixed number

Arte-miy333 [17]

5 x 3/4 = 15/4

15/4 = 3 3/4

6 0

3 years ago

A Shop sells two different bags of rice .

DIA [1.3K]

Answer:

b gives you more free rice

Step-by-step explanation:

....hope it helps

inform if wrong!!

8 0

3 years ago

What is the product in simplest form? State any restrictions on the variable. Please show your work.

mote1985 [20]

You have the following expressions given in the problem above:

(y^2/y-3)(y^2-y-6/y^2+y)

By applying the exponents properties, you can simplify it, as it shown below:

(y^2/y-3)(y^2-y-6/y^2+y)
(y^4-y^3-6y^2)/(y^3+y^2-3y2-3y)
(y^4-y^3-6y^2)/(y^3-2y2-3y)

Then, you have:
y^2(y^2-y-6)/y(y^2-2y-3)
(y^2-y-6)/(y^2-2y-3)

The answer is: (y^2-y-6)/(y^2-2y-3)

5 0

3 years ago

Read 2 more answers

Can someone help me on this please.

kiruha [24]

Answer: 7x1.5=10.5

Step-by-step explanation:

Bc i know

8 0

2 years ago

Read 2 more answers

What is unsustainable commercial​

What is unsustainable commercial