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Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) ? 0.]f(x) = 10/x , a= -2f(x) = \sum_{n=0}^{\infty } ______Find the associated radius of convergence R.R = ______

Answers

Answer 1
Answer:

Rewrite f as

f(x)=\frac{10}x=-\frac5{1-\frac{x+2}2}

and recall that for |x|<1, we have

\displaystyle\frac1{1-x}=\sum_(n=0)^\infty x^n

so that for \left|\frac{x+2}2\right|<1, or |x+2|<2,

f(x)=-5\displaystyle\sum_(n=0)^\infty\left(\frac{x+2}2\right)^n

Then the radius of convergence is 2.
Answer 2
Answer:

Final answer:

The Taylor series for the function f(x) = 10/x, centered at a = -2, is given by the formula  ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence (R) for the series is ∞, which means the series converges for all real numbers x.

Explanation:

Given the function f(x) = 10/x, we're asked to find the Taylor series centered at a = -2. A Taylor series of a function is a series representation which can be found using the formula f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + .... For f(x) = 10/x, the Taylor series centered at a = -2 will be ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence R is determined by the limit as n approaches infinity of the absolute value of the ratio of the nth term and the (n+1)th term. This results in R = ∞, indicating the series converges for all real numbers x.

Learn more about Taylor series here:

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Answers

9514 1404 393

Answer:

  45. (8√2)∠π/4

  46. (7√2)∠3π/4

Step-by-step explanation:

The polar form of a+bi is ...

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__

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Additional comment

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Factor 48e + 180 using gcf

Answers

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The gcf is 12, so you'll divide 12 to both the 48 and the 180.

So it'll look like this...

12(4e+15)

P.S. don't forget to the "e"

If you want to check if you're right just distribute the 12 and you should get 48e + 180 if you didn't you did something wrong.

Enter the number that belongs in the green box

Answers

Answer:

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Step-by-step explanation:

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Alex buys six equally priced candy bars for $9:00 what is the unit rate?
​

Answers

Answer:

$1.5 unit

Step-by-step explanation:

According to the given situation, the calculation of the unit rate is shown below:-

Candy bars = 6

Amount of candy bars = $9:00

Unit rate

= (Amount\ of\ candy\ bars)/(Number\ of\ candy\ bars)

Now we will put the values into the above formula

= (\$9:00)/(6)

Which gives result

= $1.5 unit

Therefore for computing the unit rate we simply divide the amount of candy bars by the number of candy bars.

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Answers

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Answers

Answer:

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Step-by-step explanation:

5.16/4=1.29
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