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Oksana_A [137]
3 years ago
13

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

Mathematics
1 answer:
Mice21 [21]3 years ago
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

#SPJ1

5 0
2 years ago
Read 2 more answers
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
2 years ago
Solve.<br> X = -7<br> 4x - 4y = 12<br> (x,y)
Fynjy0 [20]

Answer:

(-7, -10)

x=-7\\y=-10

Step-by-step explanation:

4x-4y=12

Substitute x for -7.

4(-7)-4y=12

Multiply 4 by -7.

-28-4y=12

Add 28 on both sides.

-4y=40

Divide -4 on both sides.

y=-10

4 0
3 years ago
2x+y=7 NEED HELP WITH THIS EQUATION
gogolik [260]

x=\frac{7-y}{2}

y=7−2x

6 0
3 years ago
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Use the following equations to solve the problem.
Liono4ka [1.6K]
35 mph = 56 km/h

Final distance = 11.3 + 56 x 3
Final distance = 179.3 km

The second option is correct.
3 0
3 years ago
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