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cupoosta [38]
2 years ago
7

Find a power series representation for the function. (Assume a>0. Give your power series representation centered at x=0 .)

Mathematics
1 answer:
melamori03 [73]2 years ago
7 0

Answer:

Step-by-step explanation:

Given that:

f_x = \dfrac{x^2}{a^7-x^7}

= \dfrac{x^2}{a^7(1-\dfrac{x^7}{a^7})}

= \dfrac{x^2}{a^7}\Big(1-\dfrac{x^7}{a^7} \Big)^{-1}

since  \Big((1-x)^{-1}= 1+x+x^2+x^3+...=\sum \limits ^{\infty}_{n=0}x^n\Big)

Then, it implies that:

\implies  \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\Big(\dfrac{x}{a} \Big)^{^7} \Big)^n

= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x}{a} \Big)^{^{7n}}

= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x^{7n}}{a^{7n}} \Big)}

\mathbf{=  \sum \limits ^{\infty}_{n=0} \dfrac{x^{7n+2}}{a^{7n+7}} }}

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Rasek [7]

The question is incomplete. Below you will find the missing graph.

The lowest value of the range of the function shown on graph is (B) -2.

Graph is the pictorial representation of the function or mathematical relation.

The lowest value of the graph is the value of y when y=f(x) gives the least value.

From the given graph we can clearly see that at x=3 the graph of the given function approaches the least value which is -2.

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2 years ago
Brenda throws a dart at this square-shaped target:
Klio2033 [76]

Answer: See below

Step-by-step explanation:

<u>Area of the square</u>  = l*w = 11*11 = 121  

<u>Area of the circle</u>  = pi r^2 = pi*1^2 =  3.142

<u>Part A</u>

P(hitting the circle) = 3.142 / 121  =  0.026 which is closer to 0.

<u>Part B</u>

P(hitting the outside portion)  = 1 - 0.026 = 0.974 which is closer to 1.  

4 0
2 years ago
Read 2 more answers
The Jones family has saved a maximum of $750 for their family vacation to the beach.  While planning the trip, they determine th
Lemur [1.5K]

Answer:

Value of h greater than 5.4 will make inequality false.

Step-by-step explanation:

This question is incomplete; here is the complete question.

The Jones family has saved a maximum of $750 for their family vacation to the beach. While planning the trip, they determine that the hotel will average $125 a night and tickets for scuba diving are $75. The inequality can be used to determine the number of nights the Jones family could spend at the hotel 750 ≥ 75 + 125h. What value of h does NOT make the inequality true?

From the given question,

Per night expense (expected) = $125

If Jones family stays in the hotel for 'h' days then total expenditure on stay = $125h

Charges for scuba diving = $75

Total charges for stay and scuba diving = $(125h + 75)

Since Jones family has saved $750 for the vacation trip so inequality representing the expenses will be,

125h + 75 ≤ 750

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h ≤ \frac{675}{125}

h ≤ 5.4

That means number of days for stay should be less than equal to 5.4

and any value of h greater than 5.4 will make the inequality false.

3 0
2 years ago
What is equivalent to<br> (6x+4y)-2y
Advocard [28]

Answer:

if the question is (6x+4y) -  2y

6x+2y or 3x+y

but if its (6x+4y)(-2y)

-6xy+(-8y)

Step-by-step explanation:

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3 years ago
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Crazy boy [7]

Answer:

f(3) = 7

Step-by-step explanation:

Substitute x = 3 into f(x) , that is

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8 0
2 years ago
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