Tiffany wanted belgian waffles for breakfast while on her dream vacation.

Mathematics

2 answers:

krek1111 [17]2 years ago

5 0

Answer:

A) belgian

Step-by-step explanation:

Belgian is a proper noun

egoroff_w [7]2 years ago

4 0

Answer: a

Step-by-step explanation: its definitly not d becuse you cannot capitilize it in the middle of a sentence/and its not waffles (the same reason) and i do not think its vacation

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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

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

5 0

2 years ago

Limited time . 10 points

AfilCa [17]

Answer:

Therefore the value of x is

$x=1\pm\sqrt{19}i$

Step-by-step explanation:

Given:

$x^{2}+20=2x$ which is

$x^{2}-2x+20=0$

To Find:

x = ? using Quadratic Formula

Solution:

For a Quadratic Equation ax² + bx + c = 0 , Formula Method is given as

$x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

On Comparing with above we get

$a=1\\b=-2\\c=20$

Substituting a , b , c in Formula method we get

$x=\dfrac{-(-2)\pm\sqrt{(-2)^{2}-4(1)(20)}}{2\times 1}\\\\x=\dfrac{2\pm\sqrt{-76}}{2}\\\\x=\dfrac{2\pm2\sqrt{19}i}{2}\\Dividing\ by\ 2\ we\ get\\\\x=1 \pm\sqrt{19}i$