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kirza4 [7]
3 years ago
6

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

ot show that Rn(x) → 0.] Find the associated radius of convergence R. f(x) = 6(1 − x)−2
Mathematics
1 answer:
weeeeeb [17]3 years ago
6 0

I guess the function is

f(x)=\dfrac6{(1-x)^2}

Rather than computing derivatives of f, recall that for |x|, we have

g(x)=\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n

Notice that

g'(x)=\dfrac1{(1-x)^2}

so that f(x)=6g'(x). Then

f(x)=6\displaystyle\sum_{n=0}^\infty nx^{n-1}=6\sum_{n=1}^\infty nx^{n-1}=6\sum_{n=0}^\infty(n+1)x^n

also valid only for |x|, so that the radius of convergence is 1.

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A line passes through (-6,-1) and (3,2).What is the equation of the line?
Lina20 [59]

Answer:

y = (1/3)x + 1

Step-by-step explanation:

You first find the slope:

(2 - (-1))/(3 - (-6)) =

3/9 =

1/3

This means the equation of the line is y = (1/3)x + b, where b is a real number.

Plug in either of the points to find the value of b:

-1 = (1/3)(-6) + b -->

-1 = -2 +b -->

1 = b

This means the equation is y = (1/3)x + 1

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3 years ago
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galina1969 [7]
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2 years ago
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6w-y=2z, Solve for the value of w
Lerok [7]
6w-y=2z 6w=2z+y w=(2z+y):6 w=(z:3)+(y:6)
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Due in 30 minutes!!<br><br> Thank you:)
Fynjy0 [20]

Answer:

The 3rd one as it's cubic

8 0
2 years ago
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20 POINTS!!!!!!
Crazy boy [7]
You will need three roots for this, so we have
Let x = -30, -10 and +20
So the factors will be (x+30)(x+10)(x-20)
The divide it to 100, this will help bring the peak up and down
So the polynomial function R(x) will become
1/100 * (x+30)(x+10)(x-20)
R(x) = 1/100 * (x+30)(x+10)(x-20)

Finding the X-intercept:
Let R(x) = 0 and solve for x.
1/100 * (x+30)(x+10)(x-20) = 0
x = -30, -10, 20 are the x-intercepts.

8 0
3 years ago
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