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2 years ago

HELP

Mathematics

2 answers:

Lapatulllka [165]2 years ago

5 0

Logxy =1/2

10^1/2=xy
Square root of 10=xy

JulijaS [17]2 years ago

5 0

Answer:

Logxy =1/2

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

3 years ago

6-x/4=x/8<br> solve for x

mina [271]

Answer:

Hope this helps

Step-by-step explanation:

x = 16

5 0

2 years ago

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A survey of pet owners found that on average, they spend $1,225 annually per pet, with a standard deviation of $275. Between whi

earnstyle [38]

Answer:

B.$675 and $1,775

Step-by-step explanation:

8 0

3 years ago

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What is the distance between A(0, 5) and B(5, -7) ?

lord [1]

Answer:

The distance between the two points is 13 units.

Step-by-step explanation:

take the test

4 0

2 years ago

WHATS THE FRACTION FOR 6 DOLLARS AND 14 CENTS

Jet001 [13]

Answer:

$6\frac{14}{100}$

Step-by-step explanation:

First, you make fourteen a fraction.

$\frac{14}{100}$

Then, make it a mixed fraction by adding a six.

$6\frac{14}{100}$

Lastly, have a great day! :)

3 0

2 years ago