2 years ago

Write a polynomial of degree 3 that satisfies each of the given conditions.

Mathematics

1 answer:

shutvik [7]2 years ago

5 0

Answer:

https://www.jacksonsd.org/cms/lib/NJ01912744/Centricity/Domain/504/BI%207-8.pdf

Step-by-step explanation:

the link to help you with the answers

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2 years ago

1. Find the length of the leg, X. If your answer is not an integer, leave it in simplest radical form (picture 1)

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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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2 years ago

Maria and her friends ate 5/8 of the 16 oranges that were at Maria's house. which is a reasonable answer for 5/8 x 16? please he

neonofarm [45]

Answer:

Step-by-step explanation:

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Nonamiya [84]

Answer:

Step-by-step explanation:

2 functions start by making a domain

Function 1: -3≤x<1

Function 2: -1≤x≤1

Now come up with equations

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Function 2= 5

Now put it all together

f(x)= x+3 for -3≤x<1 and 5 for -1≤x≤1

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2 years ago