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nataly862011 [7]
1 year ago
13

Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more

than once). give the interval of convergence for the resulting series
Mathematics
1 answer:
dalvyx [7]1 year ago
7 0

The power series  is

g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....

To deduce the power series of g(x) from the power series for f(x) and identify its radius of convergence

The power series for f(x) is just the geometric series derived from 1/1-y ,setting y=2x.

Its radius of convergence is 0.5

Let,

f(x)= 1/1-2x = 1+ (2x) + (2x)2 + .........+(2x)n......+....

The power series expansion (geometric series),

valid for I2xI < 1 , IxI < 0.5

so, radius of convergence = 0.5

The power series for g(x) is found by integrating term by term the power series of f(x) (upto a constant). The radius of converngence of g(d) is the same as that of f(x) (from general theory) =0.5

Now, g(x) = ln(1-2x)

= -2 \int\limits^a_b {(1/1-2x)} \, dx = -2 \int\limits^a_b {f(x)} \, dx

=-2 \int\limits^a_b {[1+(2x)+ (2x)2 +........+ (2x)n+.......]} \, dx

g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....

is the power series expansion for g(x).

radius of convergence =0.5

For more information about power series, visit

brainly.com/question/17225810

#SPJ4

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1.848 × 10^-2

Step-by-step explanation:

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(6 × 10^-3) × (3.08 × 10^0) = 18.48 × 10^-3 = 1.848 × 10^-2

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D 81 pi units^2

Step-by-step explanation:

The circumference of a circle  is given by

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Two people are standing on opposite sides of a hill. Person A makes an angle of elevation of 65° with the top of the hill and pe
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Answer:

Option 3. 71 ft. is the distance between B and top of the hill.

Step-by-step explanation:

Let the height of the hill is h ft and the distance of A from the hill be x ft and distance from B to hill is y.

It is given distance between A and B is 45 ft. ∠BAO = 65° and ∠ABO = 80°.

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Now from ΔACO tan 65 = \frac{h}{45-x} = 2.14

h=2.14(45-x)

From ΔBCO tan80 = \frac{h}{x} = 5.67

h = 5.67x

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A machine at a manufacturing plant can make 16 of Item A and 20 of Item B per hour. The machine runs 24 hours a day. Yesterday,
Anvisha [2.4K]

Answer:

A) x + y = 24 and 16x + 20y = 434

B) Item A = 11.5 hours per day

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Step-by-step explanation:

A) Let x represent the amount of hours it took to make item A and let y represent the amount of hours it took to make item B.

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