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3 years ago

Anyone willing to answer this question?

Mathematics

1 answer:

Vilka [71]3 years ago

4 0

Answer:

give me a second and i will answer it

Step-by-step explanation:

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SOLUTION We observe that f '(x) = -1 / (1 + x2) and find the required series by integrating the power series for -1 / (1 + x2).

Ann [662]

Answer:

Required series is:

$\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

Step-by-step explanation:

Given that

$f'(x) = -\frac{1}{1 + x^{2}}$ ---(1)

We know that:

$\frac{d}{dx}(tan^{-1}x)=\frac{1}{1+x^{2}}$ ---(2)

Comparing (1) and (2)

$f'(x)=-(tan^{-1}x)$ ---- (3)

Using power series expansion for $tan^{-1}x$

$f'(x)=-tan^{-1}x=-\int {\frac{1}{1+x^{2}} \, dx$

$= -\int{ \sum\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx$

$= -\sum{ \int\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx$

$=-[c+\sum\limits^{ \infty}_{n=0} (-1)^{n}\frac{x^{2n+1}}{2n+1}]$

$=C+\sum\limits^{ \infty}_{n=0} (-1)^{n+1}\frac{x^{2n+1}}{2n+1}$

$=C-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

$tan^{-1}(0)=0 \implies C=0$

Hence,

$\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

7 0

4 years ago

1/2 x 2 1/2 as a fraction in simplest form plz help fast

Naily [24]

5/4. first, convert the mixed fraction into an improper fraction to get 5/2. multiply the 5/2 to the 1/2. multiplying the numerators gets you 5. the denominators being multiplied gets you 4. 5 is the new numerator, 4 is the new denominator. 5/4 is in simplest form

7 0

3 years ago

175 pages in 5 days = __ pages in 2 days

barxatty [35]

In 5 days, = 175 pages
so, in 1 day = 175/5 Pages

Now, In 2 days, it would be: 175/5 * 2 = 35 * 2 = 70

So, your final answer is 70

Hope this helps!

8 0

4 years ago

Read 2 more answers

What is the average rating for operative effectiveness for national group for all 5 weeks 3.5 3.5 3.8 3.7 3.4

dsp73

Answer:

3.58

Step-by-step explanation:

You must add up all of the numbers which will get you 17.9

Then divide 17.9 by the total amount of numbers (5) = 3.58

7 0

3 years ago

Look at this set of ordered pairs.

sasho [114]

3,3,4,4,7,11,11,12,13

7 0

4 years ago