Convert 65,000,000 to scientific notation please help!!

1 answer:

3 0

You have to move the decimal point from the end to between the 6 and 5 then count how many spaces you moved it because this will become the power on the 10.
6.5 x 10^7

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Find a power series representation for the function

Mars2501 [29]

$f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}$ is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺². This can be obtained by using power series representation of each terms, sin x, eˣ and substituting in the function.

<h3>Find the power series representation for the function:</h3>

In the question the given function is,

⇒ f(x) = x³sin(x) + e³ˣ⁺²

We know that series representation of sin x and eˣ are:

$sin x = \sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1}$

$e^{x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}$

⇒ $e^{3x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}$

= $\sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}$

Substituting the series representation in the function we get,

⇒ f(x) = x³sin(x) + e³ˣ⁺²

⇒ $f(x)=x^{3}\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}$

$f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}$

Hence $f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}$ is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺².

Learn more about power series representation here:

brainly.com/question/11606956

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5 0

2 years ago

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What is the range of function g if g(x) =-2f(x-3)

chubhunter [2.5K]

Answer:

If you entered the function correctly there is not a range

Step-by-step explanation:

4 0