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love history [14]
3 years ago
10

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive an

y points for the skipped part, and you will not be able to come back to the skipped part.
Find a power series representation for the function. Determine the interval of convergence. (Give your power series representation centered at x=0)
f(x)=1/6+x
Mathematics
1 answer:
GaryK [48]3 years ago
4 0

Answer:

The series representation is \sum_{n=0}^{\infty}(-1)^n\frac{x^n}{6^{n+1}} and the interval of convergence is (-6,6)

Step-by-step explanation:

We want to find a series, such that f(x) = \sum_{n=0}{\infty}a_n(x-a)^{n}[/tex], were a is the value that we are using to center the series expansion. In our case, a=0.

We will use the geometric series formula as follows. For |r|<1 then

\frac{1}{1-r}=\sum_{n=0}^{\infty} r^n

In our case, with some algebreaic manipulation we have that

f(x) = \frac{1}{6+x} = \frac{1}{6}\frac{1}{1-(\frac{-x}{6})}

Taking r = \frac{-x}{6} we get that

f(x) = \frac{1}{6}\sum_{n=0}^{\infty} (\frac{-x}{6})^n = \sum_{n=0}^{\infty}(-1)^n\frac{x^n}{6^{n+1}}

This representation is valid (that means that the series converges to the value of f(x)) only for |r|<1. That is

\left|\frac{-x}{6}\right|= \left|\frac{x}{6}\right|

which implies that |x|<6. So the interval of convergence is (-6,6).

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If $5000 is invested at a rate of 3% interest
harkovskaia [24]

The value of the investment in 5 years is $5805.9

<h3>What is Interest ?</h3>

Interest is the amount earned over years for the amount invested.

It is given that

Principal = $5000

Rate = 3%

Compounded Quarterly

Time = 5 years

Amount = ?

The Amount is given by the formula

Amount = P( 1 + (r/n))ⁿˣ

Here n = t = time period for which the investment has been done.

Amount = 5000( 1+(3/4 * 100)⁴ˣ⁵

Amount = 5000 (1.16)

Amount = $ 5805.9

Therefore , The value of the investment in 5 years is $5805.9

To know more about Interest

brainly.com/question/13324776

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7 0
2 years ago
Please help Need answer Urgently.
KIM [24]
Answer is C
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a car traveled 36 miles in 45 minutes. the car traveled at a constant speed. it the car continues to travel at this rate which e
Alchen [17]
Y = 48 becuase you travelled the amount of minuets 45 x
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3 years ago
The division of whole numbers is commutative. true or false?
AURORKA [14]
'Commutative' means you can work it in the other direction without changing it.
But 1/2 is not the same number as 2/1 . So I guess division is NOT commutative.
3 0
3 years ago
What’s the compound inequality for this??
MariettaO [177]

Answer:

-2 < x<4

Step-by-step explanation:

We have open circles and -2 and 4 so we don't include those numbers

The line is in between so the x is in between

-2 < x<4

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