4 years ago

Which of the following statements is not true?

Mathematics

1 answer:

bezimeni [28]4 years ago

6 0

All of the above are true

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If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.

Pie

Given that $f^{(n)}(0)=(n+1)!$ , we have for $f(x)$ the Taylor series expansion about 0 as

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

Replace $n+1$ with $n$ , so that the series is equivalent to

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}$

and notice that

$\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}$

Recall that for $|x|$ , we have

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

which means

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}=\frac{\mathrm d}{\mathrm dx}\frac1{1-x}$
$\implies f(x)=\dfrac1{(1-x)^2}$

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3 years ago

PLZ HELP 50 POINTS AND BRAINLIEST

Roman55 [17]

Answer:

adjacent and supplementary

Step-by-step explanation:

∠ 1 and ∠ 2 are next to each other, that is adjacent.

∠ 1 and ∠ 2 form a straight angle and are supplementary.

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3 years ago

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Three ounces of cinnamon cost $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?

Nikolay [14]

$12.80 is your answer.. see all you needed to do was divide $2.40 by three.. as that is one oz you would only then multiply by twelve for your answer.

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tia_tia [17]

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3 years ago

I need the answer asap!!!! thanks!

vova2212 [387]

Y=-7/2x+1/2

i already typed the work out but something went wrong?
1. find slope
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3 years ago