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3 years ago

Solve -3h(4h^2+2h-4)

Mathematics

1 answer:

Rama09 [41]3 years ago

5 0

Answer:

-12h^3-6h^2+12h

Step-by-step explanation:

-3h(4h^2+2h-4)

-12h^3-6h^2+12h

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Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). What is the radius of convergence? (Note

Viktor [21]

a. Recall that

$\displaystyle\int\frac{\mathrm dx}{1-x}=-\ln|1-x|+C$

For $|x|$ , we have

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

By integrating both sides, we get

$\displaystyle-\ln(1-x)=C+\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

If $x=0$ , then

$\displaystyle-\ln1=C+\sum_{n=0}^\infty\frac{0^{n+1}}{n+1}\implies 0=C+0\implies C=0$

so that

$\displaystyle\ln(1-x)=-\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

We can shift the index to simplify the sum slightly.

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

b. The power series for $x\ln(1-x)$ can be obtained simply by multiplying both sides of the series above by $x$ .

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

c. We have

$\ln2=-\dfrac\ln12=-\ln\left(1-\dfrac12\right)$

$\displaystyle\implies\ln2=\sum_{n=1}^\infty\frac1{n2^n}$

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3 years ago

Does this graph represent a proportional relationship?<br> Explain.

Ugo [173]

ANSWER: no

EXPLAIN: because a proportional relationship graph would have a straight line running through the origin

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evablogger [386]

For this case we must indicate the correct sign between the following numbers:

$\frac {11} {18}\ and\ \frac {17} {24}$

We have to:

$\frac {11} {18} = 0.611111111111\\\frac {17} {24} = 0.708333333333$

So, we have to $\frac {17} {24}> \frac {11} {18}$

Answer:

$\frac {17} {24}> \frac {11} {18}$

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Step-by-step:

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