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Reil [10]
3 years ago
8

Find the Taylor series for f(x) centered at the given value of a. (Assume that f has a power series expansion. Do not show that

Rn(x)→0 . f(x)=lnx, a=
Mathematics
1 answer:
Kobotan [32]3 years ago
3 0

Answer:

Here we just want to find the Taylor series for f(x) = ln(x), centered at the value of a (which we do not know).

Remember that the general Taylor expansion is:

f(x) = f(a) + f'(a)*(x - a) + \frac{1}{2!}*f''(a)(x -a)^2 + ...

for our function we have:

f'(x) =  1/x

f''(x) = -1/x^2

f'''(x) =  (1/2)*(1/x^3)

this is enough, now just let's write the series:

f(x) = ln(a) +  \frac{1}{a} *(x - a) - \frac{1}{2!} *\frac{1}{a^2} *(x - a)^2 + \frac{1}{3!} *\frac{1}{2*a^3} *(x - a)^3 + ....

This is the Taylor series to 3rd degree, you just need to change the value of a for the required value.

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Step-by-step explanation:

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6 0
3 years ago
A cylindrical swimming pool has a diameter of 20 feet and a height of 3.5 feet. How many gallons of water can the pool contain?
kvasek [131]

Answer:

The swimming pool will contain approx 8243\ gal of water.

Step-by-step explanation:

Given the swimming pool is in a cylindrical shape.

And the dimensions are 20\ feet diameter with a height of 3.5\ feet.

Also, 1\ ft^3 =7.5\ gal

First, we will find the volume of the swimming pool.

The swimming pool is in cylindrical shape.

So, the volume would be \pi r^2h

The height (h) is given as 3.5\ feet. To calculate radius (r) we will divide the diameter by two.

The radius of the cylinder would be \frac{20}{2}=10\ feet

Plug these values in the formula we get,

\pi r^2h\\=\pi\times 10^2\times 3.5\\=3.14\times 100\times 3.5\\=1099\ ft^3

Now, it is given 1\ ft^3 =7.5\ gal

So, 1099\ ft^3 =1099\times 7.5\ gal=8242.5\ gal

The swimming pool will contain approx 8243\ gal of water.

6 0
3 years ago
Samuel filled the glasses shown below completely with water. The total amount of water that Samuel poured into the glasses is 60
Rama09 [41]
The height of the cylinder (glass 1) we call h so the volume is 4πh cc.
The volume of the cone is ⅓×2.5²×6π=12.5π cc.
If we divide 60 by π we get 19.11 cc approx.
So 4h+12.5=19.11, 4h=6.61 cc and h=1.7 cm approx, answer 2.
3 0
3 years ago
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Answer this question for points
Arte-miy333 [17]

Answer:

102 or the 12th number considering 38 is the 4th

3 0
2 years ago
Rewrite the equation for x, and express its value in terms of a. 3/a x - 4 = 20
My name is Ann [436]

For this case, we must clear variable "x" from the given equation, expressed in terms of "a".

We have:

3/a x-4=20

By clearing "x" we have:

Adding 4 to both sides of the equation:

3/a x = 20 + 4

Multiplying by a/3 on both sides of the equation:

x=24a/3

x=8a

So, x=8a

Answer:

x=8a

7 0
3 years ago
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