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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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6 - 2y + (-8y) + 5.1 = 0<br> (Simplify your answer. Use integers
Nadusha1986 [10]

Answer:

Simplified answer = 11.1 - 10y = 0

y = 1.11

Step-by-step explanation:

6 - 2y + (-8y) + 5.1 = 0

6 + 5.1 -2y -8y = 0

Add like terms

11.1 - 10y = 0

(This is simplified, but if you want to solve for y, continue)

11.1 - 10y = 0

÷10  ÷10

1.11 - y = 0

y = 1.11 because 1.11 - 1.11 is 0

I Hope That This Helps!

8 0
3 years ago
Which strategy would you choose to expand (x+11)(2x+3) and write an equivalent expression
Vlad1618 [11]

Answer:

Step-by-step explanation:

Given the expression (x+11)(2x+3)

We want to expand it and write equivalent expression

Generally if we want to expand an expression we will take one of the expression in one bracket and multiply with the other bracket and then take the other expression and multiply it with the other

E.g, (a+b) × (c + d)

Then, we take a × (c+d) and also b × (c+d)

We can do it the other way round too and it will give the same results.

So, applying this to the given expression

(x+11)(2x+3)

x(2x+3) + 11(2x+3)

2x² + 3x + 22x + 33

2x² + 25x + 33

Then, the equivalent expression is 2x² + 25x + 33

(x + 11)(2x + 3) = 2x² + 25x + 33

5 0
3 years ago
Answer pls thank you
Luba_88 [7]

Step-by-step explanation:

l

  1. lcm 3
  2. use the lcm to divide the answers by 3

7 0
2 years ago
The equation of a straight line is 3y + 9x -12 =0. Use the equation to find the
Debora [2.8K]

Answer:

-3

Step-by-step explanation:

Divide through the equation by the leading coefficient to obtain:

y+3x-4=0

y=4-3x

and our gradient is -3

3 0
3 years ago
Pani says she should get $3 discount on the price of each shirt and a $3 discount on the price of each pair of jeans. Write and
PilotLPTM [1.2K]

Answer:

(S - 3) + (X - 3) = B

Step-by-step explanation:

S = amount of shirts

X = amount of jeans

B = total amount she would pay

(S - 3) + (X - 3) = B



5 0
3 years ago
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