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grigory [225]
2 years ago
12

Name three exponent rules

Mathematics
2 answers:
Nikitich [7]2 years ago
5 0

Answer:

Quotient rules

Derivative rule

Negative exponents

hope this helps

belka [17]2 years ago
3 0
Three examples of exponent rules are;

Product of Powers Rule
Quotient of Powers Rule
Power of a Power Rule

Hope this helps!
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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
2 years ago
What is the least common multiple of 8, 25, and 40?
snow_lady [41]

Answer:200

Step-by-step explanation:

5 0
1 year ago
Can someone help with question 3
kirza4 [7]

Answer:

This is what you have to explain:

With 5n, you are multiplying a number and a variable.

With 5 + n, you are adding a number and a variable.

4 0
3 years ago
1 point
Ber [7]
15
Explanation:
you just divide 90 by 6
6 0
2 years ago
The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounce. We are interested in testing to de
noname [10]

Answer:

Should not be rejected.

Step-by-step explanation:

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