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3 years ago

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What is 3 to the power of 3 over 2 equal to? (5 points) Select one: a. cube root of 9 b. square root of 9 c. cube root of 27 d.

square root of 27

1 answer:

romanna [79]3 years ago

8 0

(3^3)/2=13.5
Hope this helps you..!!!!

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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

FromTheMoon [43]

Answer:

The Taylor series is $\ln(x) = \ln 3 + \sum_{n=1}^{\infty} (-1)^{n+1} \frac{(x-3)^n}{3^n n}$ .

The radius of convergence is $R=3$ .

Step-by-step explanation:

<em>The Taylor expansion.</em>

Recall that as we want the Taylor series centered at $a=3$ its expression is given in powers of $(x-3)$ . With this in mind we need to do some transformations with the goal to obtain the asked Taylor series from the Taylor expansion of $\ln(1+x)$ .

Then,

$\ln(x) = \ln(x-3+3) = \ln(3(\frac{x-3}{3} + 1 )) = \ln 3 + \ln(1 + \frac{x-3}{3}).$

Now, in order to make a more compact notation write $\frac{x-3}{3}=y$ . Thus, the above expression becomes

$\ln(x) = \ln 3 + \ln(1+y).$

Notice that, if x is very close from 3, then y is very close from 0. Then, we can use the Taylor expansion of the logarithm. Hence,

$\ln(x) = \ln 3 + \ln(1+y) = \ln 3 + \sum_{n=1}^{\infty} (-1)^{n+1} \frac{y^n}{n}.$

Now, substitute $\frac{x-3}{3}=y$ in the previous equality. Thus,

$\ln(x) = \ln 3 + \sum_{n=1}^{\infty} (-1)^{n+1} \frac{(x-3)^n}{3^n n}.$

<em>Radius of convergence.</em>

We find the radius of convergence with the Cauchy-Hadamard formula:

$R^{-1} = \lim_{n\rightarrow\infty} \sqrt[n]{|a_n|},$

Where $a_n$ stands for the coefficients of the Taylor series and $R$ for the radius of convergence.

In this case the coefficients of the Taylor series are

$a_n = \frac{(-1)^{n+1}}{ n3^n}$

and in consequence $|a_n| = \frac{1}{3^nn}$ . Then,

$\sqrt[n]{|a_n|} = \sqrt[n]{\frac{1}{3^nn}}$

Applying the properties of roots

$\sqrt[n]{|a_n|} = \frac{1}{3\sqrt[n]{n}}.$

Hence,

$R^{-1} = \lim_{n\rightarrow\infty} \frac{1}{3\sqrt[n]{n}} =\frac{1}{3}$

Recall that

$\lim_{n\rightarrow\infty} \sqrt[n]{n}=1.$

So, as $R^{-1}=\frac{1}{3}$ we get that $R=3$ .

8 0

4 years ago

..................<br>..

natali 33 [55]

Answer:

The answer is C 18

Step-by-step explanation:

4^2+8/4= 16+2=18

3 0

4 years ago

To get ready for a field trip students and adults are put into groups for every 12 students in a group there are 2 adults if the

Slav-nsk [51]

If you multiply the number of students times 8 you get 96, but if you multiply the students by 8 you need to multiply the adults by 8 as well. Which leaves you with 16 adults. Is there more to this equation? I feel like this is only part of it.

3 0

3 years ago

Is c the correct answer or?

vodka [1.7K]

I think yes it's correct but I'm not sure.

7 0

3 years ago

Read 2 more answers

Find the coordinates of the point three tenths<br><br> of the way from A(-4, -8) to B(11, 7)

Leviafan [203]

let's first off take a peek at those values.

let's say the point with those coordinates is point C, so C is 3/10 of the way from A to B.

meaning, we take the segment AB and cut it in 10 equal pieces, AC takes 3 pieces, and CB takes 7 pieces, namely AC and CB are at a 3:7 ratio.

$\bf ~~~~~~~~~~~~\textit{internal division of a line segment}
\\\\\\
A(-4,-8)\qquad B(11,7)\qquad
\qquad \stackrel{\textit{ratio from A to B}}{3:7}
\\\\\\
\cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{7}\implies \cfrac{A}{B} = \cfrac{3}{7}\implies 7A=3B\implies 7(-4,-8)=3(11,7)\\\\[-0.35em]
~\dotfill\\\\
C=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em]
~\dotfill$

$\bf C=\left(\cfrac{(7\cdot -4)+(3\cdot 11)}{3+7}\quad ,\quad \cfrac{(7\cdot -8)+(3\cdot 7)}{3+7}\right)
\\\\\\
C=\left( \cfrac{-28+33}{10}~~,~~\cfrac{-56+21}{10} \right)\implies C=\left( \cfrac{5}{10}~~,~~\cfrac{-35}{10} \right)
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
~\hfill C=\left( \frac{1}{2}~,~-\frac{7}{2} \right)~\hfill$

4 0

3 years ago