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steposvetlana [31]
4 years ago
9

What is the complete factorization of the polynomial function over the set of complex numbers?

Mathematics
1 answer:
arsen [322]4 years ago
7 0
You can check this answer.

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Consider the function f given by f(x)=x*(e^(-x^2)) for all real numbers x.
NISA [10]

Answer:

\frac{\sqrt{\pi}}{4}

Step-by-step explanation:

You are going to integrate the following function:

g(x)=x*f(x)=x*xe^{-x^2}=x^2e^{-x^2}  (1)

furthermore, you know that:

\int_0^{\infty}e^{-x^2}=\frac{\sqrt{\pi}}{2}

lets call to this integral, the integral Io.

for a general form of I you have In:

I_n=\int_0^{\infty}x^ne^{-ax^2}dx

furthermore you use the fact that:

I_n=-\frac{\partial I_{n-2}}{\partial a}

by using this last expression in an iterative way you obtain the following:

\int_0^{\infty}x^{2s}e^{-ax^2}dx=\frac{(2s-1)!!}{2^{s+1}a^s}\sqrt{\frac{\pi}{a}} (2)

with n=2s a even number

for s=1 you have n=2, that is, the function g(x). By using the equation (2) (with a = 1) you finally obtain:

\int_0^{\infty}x^2e^{-x^2}dx=\frac{(2(1)-1)!}{2^{1+1}(1^1)}\sqrt{\pi}=\frac{\sqrt{\pi}}{4}

5 0
3 years ago
Read 2 more answers
What is 2 + -5 - -13
rosijanka [135]

Answer:

10.

The answer is 10.

5 0
3 years ago
Read 2 more answers
The sum of the angle measures of any triangle is
romanna [79]
Let's say that y is the unknown
180=2x+3+5x+1+y
180=7x+4+y
180-7x-4=y
176-7x=y=third angle
3 0
3 years ago
75% of the children at Fisher Elementary walk to school. If there are 200 students at Fisher Elementary, how many walk to school
BlackZzzverrR [31]

Answer: 150 students walk to school

Step-by-step explanation: 75%=0.75

200 multiplied by 0.75

 200×0.75=150 students

            Or

75%=3/4

3/4 of the children walk to school

3/4×200=3/4×200/1=150

4 0
3 years ago
Describe the correct error -1/4 divided by 3/2=-4/1 multiplied by 3/2= -12/2=-6
Rom4ik [11]
I guess the error is in the calculus.
-1/4 divided by 3/2:
(-1/4)/(3/2): When dividing 2 fractions, its answer is equal to the first fraction multiplied by the inverse of the second.
(-1/4)/(3/2) = -1/4 * 2/3 = -2/12
So -1/4 divided by 3/2 is different from -4/1 multiplied by 3/2.
-1/4 divided by 3/2 = -1/4 multiplied by 2/3.

Hope this Helps! :)
6 0
4 years ago
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