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topjm [15]
2 years ago
9

Using the graph of f(x) and g(x), where g(x) = f(k⋅x), determine the value of k.

Mathematics
1 answer:
baherus [9]2 years ago
3 0

Answer:

1/3

Step-by-step explanation:

This is about the interpretation of the graph

From the graph, we can see the 2 lines representing function f(x) and function g(x).

Now for us to find the value of x in g(x) = k⋅f(x), we need to get a mutual x-coordinate where we can easily read their respective y-coordinate values.

We see that the best point for that is where x = -3.

For f(x), when x = -3, y = 1

For g(x), when x = -3, y = -3

we can rewrite them as;

x = -3, f(-3) = 1 and x = -3, g(-3) = -3

Let us plug in the relevant values into g(x) = k⋅f(x) to get;

-3 = k(1)

Thus; k = -1/3

Hope it helps you mark me as brinllent

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Allushta [10]

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5 0
3 years ago
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
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Mariulka [41]

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-122<-3(-2-8x)-8x

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x>-8

5 0
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