Divided by 85 show me the work

Find a power series representation of e^x sin(x)

liberstina [14]

The Taylor series is defined by:
$f(x) = \sum \frac{f^n (a)}{n!} (x-a)^n$

Let a = 0.
Then its just a matter of finding derivatives and determining how many terms is needed for the series.

Derivatives can be found using product rule:
$f^n (x) = e^x g^{n-1} (x) + e^x g^n (x) \\ g^0 (x) = sin x$

Do this successively to n = 6.
$f^1 (x) = e^x (sinx +cos x) \\ f^2 (x) = e^x (2cos x) \\ f^3 (x) = e^x(2cos x - 2sin x) \\ f^4 (x) = e^x (-4 sin x) \\ f^5 (x) = e^x(-4sinx -4cos x) \\ f^6(x) = e^x(-8cos x)$

Plug in x=0 and sub into taylor series:
$e^x sin x = x+x^2 +\frac{x^3}{3} -\frac{x^5}{30}-\frac{x^6}{90}...$

If more terms are needed simply continue the recursive derivative formula and add to taylor series.

6 0

3 years ago

70% of 80 is what number

rosijanka [135]

It would be 56,
I wish you luck.

3 0

3 years ago

Read 2 more answers

Is 1000 a term in the sequence 50,65,80,95

Alex Ar [27]

Yes it is

it’s the 41st term

EXPLANATION:

the nth term would be 15n+35
because the terms go up by 15 and you add 35 to get to the term.

1. 2. 3. 4.
50. 65. 80. 95

1000- 35= 965

965/15=41

7 0

2 years ago

Carly tried to solve an equation step by step.

jeyben [28]

Answer:

First step of the problem

Step-by-step explanation:

The mistake that Carly did while solving the equation was that she multiplied -4 with 10, when there was no reason to. If she had to, it would be if -4 was 1 over -4 and then to get rid of that should would multiplied that on both sides. Both in this case there was no reason to.

Besides that, the real way to solve the problem is by doing these steps.

1. Distribute property

-4(7j+2) = 10 => take -4 times 7j and -4 times POSITIVE 2

-28j-8= 10

You may be wondering why can't we add 7j and 2 together? Well it's because they aren't the same variable if 7j was just 7, then you could add 7 and 2 together. And if 2 was 2j, you would add 7j and 2j together. This type of process is called "combine like terms." It's when you add or subtract all the terms that are the same variable.

2. Get "j" on one side

-28j-8= 10

-28j= 18

With this we had to add 8 on both sides to get -28j on one side of the equation. This is how we ended up with -28j= 18

3. Get "j" all alone

18

j= -28/18

or j= -14/9

Why did we divide 18? Well if you divide 18 on both sides, you have one side cancel out and the other side resulting in the coefficient with the variable divided by the number, this will cause "j" to be alone or have an answer.

The right answer for "j" is actually -14/9

I hope this help you understand, if not don't be afraid to ask questions or even comment. Hope you have a great day, bye! :D

8 0

3 years ago

Which expression is equivalent to 15 n=10 (n+3/n)?

Karolina [17]

Answer:

±√6

Step-by-step explanation:

$15n=10(n+\frac{3}{n} )$ is your expression first muiltiply out the 10 to get 15n= 10n+10 3/n next subtract 10 n from both sides to get 5n=10+3/n multiply both sides by n to get 5n^2=13 combine both sides and use the quadratic equation to solve to get your solution of ±√6

3 0

2 years ago