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Lady bird [3.3K]

3 years ago

5

Which quantity is best expressed as +5?

1 answer:

Softa [21]3 years ago

4 0

The answer is B. a profit of $5

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Evaluate using integration by parts

PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

$I(n)=\displaystyle\int x^ne^x\,\mathrm dx$

One round of IBP, setting

$u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx$

$\mathrm dv=e^x\,\mathrm dx\implies v=e^x$

gives

$\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx$

$I(n)=x^ne^x-nI(n-1)$

This is called a power-reduction formula. We could try solving for $I(n)$ explicitly, but no need. $n=5$ is small enough to just expand $I(5)$ as much as we need to.

$I(5)=x^5e^x-5I(4)$

$I(5)=x^5e^x-5(x^4e^x-4I(3))=(x-5)x^4e^x+20I(3)$

$I(5)=(x-5)x^4e^x+20(x^3e^x-3I(2))=(x^2-5x+20)x^3e^x-60I(2)$

$I(5)=(x^2-5x+20)x^3e^x-60(x^2e^x-2I(1))=(x^3-5x^2+20x-60)x^2e^x+120I(1)$

$I(5)=(x^3-5x^2+20x-60)x^2e^x+120(xe^x-I(0))$

Finally,

$I(0)=\displaystyle\int e^x\,\mathrm dx=e^x+C$

so we end up with

$I(5)=(x^4-5x^3+20x^2-60x+120)xe^x-120e^x+C$

$I(5)=(x^5-5x^4+20x^3-60x^2+120x-120)e^x+C$

and the antiderivative is

$\displaystyle\int2x^5e^x\,\mathrm dx=(2x^5-10x^4+40x^3-120x^2+240x-240)e^x+C$

8 0

3 years ago

Which of the following expressions could be equal to f(x)???

noname [10]

If i understand the machine correctly and -3 is x and 8 is the final answer, f(x)=x+11

4 0

3 years ago

Approximate the value of each of the irrational numbers below to the nearest thousandth.

Marta_Voda [28]

ANSWER

$\sqrt{13} = 3.606$

to the nearest thousandth.

EXPLANATION

The given irrational number is

$\sqrt{13}$

We use the calculator to evaluate this to obtain,

$\sqrt{13} = 3.605551...$

To round to the nearest thousandth means we are rounding to 3 decimal places.

The third decimal place is 5.

The next number is 5 so we round up.

$\sqrt{13} = 3.606$

4 0

3 years ago

Solve For Q<br><br> q/10=4<br><br> Please Answer This For Me. Thanks.

Maurinko [17]

$\frac{q}{10} = 4\\q = 4 * 10\\q = 40$

Answer: 40.

3 0

3 years ago

Read 2 more answers

Find the value of the variable in the figure provided <br><br><br> PLEASE HELP ASAP

Harlamova29_29 [7]

Answer:

x=17

Step-by-step explanation:

(5x-58)=(2x-7) ->(because of cosine-rule)

3x=51

x=17

6 0

3 years ago