Quadrilateral ABCD is inscribed in this circle.

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

Bond [772]

Taylor series is $f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }$

To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have

f(x) = ln(x)

$f^{1}(x)= \frac{1}{x} \\f^{2}(x)= -\frac{1}{x^{2} }\\f^{3}(x)= -\frac{2}{x^{3} }\\f^{4}(x)= \frac{-6}{x^{4} }$

.

Since we need to have it centered at 9, we must take the value of f(9), and so on.

f(9) = ln(9)

$f^{1}(9)= \frac{1}{9} \\f^{2}(9)= -\frac{1}{9^{2} }\\f^{3}(x)= -\frac{1(2)}{9^{3} }\\f^{4}(x)= \frac{-1(2)(3)}{9^{4} }$

.

Following the pattern, we can see that for $f^{n}(x)$ ,

$f^{n}(x)=(-1)^{n-1}\frac{1.2.3.4.5...........(n-1)}{9^{n} } \\f^{n}(x)=(-1)^{n-1}\frac{(n-1)!}{9^{n}}$

This applies for n ≥ 1, Expressing f(x) in summation, we have

$\sum_{n=0}^{\infinite} \frac{f^{n}(9) }{n!} (x-9)^{2}$

Combining ln2 with the rest of series, we have

$f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }$

Taylor series is $f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }$

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3 0

1 year ago

296.32 divided by 4= how to solve<br> pls

astraxan [27]

Hello I hope you are having a Great day :)

Your question, 296.32 divided by 4

Your answer would be 74.08

Hopefully that helps you :)

7 0

2 years ago

Read 2 more answers

Express six cups 25 quarts as a fraction in simplest form

Arada [10]

D because 6/20 is correct and the three wrong super wrong hope it helps

5 0

3 years ago

Explain how to solve 5^(x − 2) = 8 using the change of base formula log base b of y equals log y over log b.

Ray Of Light [21]

Answer:

x = 3.3

Step-by-step explanation:

A equation is given to us and we need to solve out for x. The given equation is ,

Take log on both sides with base as " 10" . We have ,

Simplify using the property of log , , we have ,

Simplify ,

Again simplify using the property of log ,

We know that log 5 = 0.69 and log 2 = 0.301 , on substituting this , we have ,

Simplify the RHS ,

Add 2 both sides ,

Hence the Value of x is 3.30 .

3 0

2 years ago

2x+1y=25 <br> find the equation of x

leonid [27]

Answer:

x=

−1

2

y+

25/2

Step-by-step explanation:

Let's solve for x.

2x+1y=25

Step 1: Add -y to both sides.

2x+y+−y=25+−y

2x=−y+25

Step 2: Divide both sides by 2.

2x

2

=

−y+25

2

x=

−1

2

y+

25

2

8 0

2 years ago

​ Quadrilateral ABCD ​ is inscribed in this circle.

Quadrilateral ABCD is inscribed in this circle.