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3 years ago

Consider the equation 3x + 1 = 2x + 5

Mathematics

1 answer:

fomenos3 years ago

3 0

You can’t technically solve it because there’s no question

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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

Use the drop-down menus to choose steps in order to correctly solve 1+2b−13=12−4b−2b1+2b-13=12-4b-2b for b

inessss [21]

5 0

3 years ago

Read 2 more answers

3xy - ² + 4x for x = -2, y = - and = 6?

Kitty [74]

Answer:

See below

Step-by-step explanation:

Not sure what you are asking....do you want to know what y is when x = -2 and the equation = 6 ?

3 xy^2 + 4x = 6 or is that 3 xy^(-2) + 4x = 6

Could use some serious editing of your question if you are able ....

7 0

2 years ago

Is each expression equivalent to 2x^2 - 50?

puteri [66]

We would first determine how to solve this, and then from there, we would then see whether the following answer would be the correct answers.

$2x^2 - 50 \\ \\ Pull \ out \ like \ factors : \\ 

 2x^2 - 50 = 2 * (x^2 - 25) \\ \\ Factoring: \\ x^2 - 25 \\ \\ (your \ answer)...\\ \\ 2 * (x + 5) * (x - 5)$

Now, we can determine whether the say "yes" or "no" to the following answers.

<span>a 2(x-5)(x+5) = YES
b -2(x+5)(x+5) = NO
c -2(5-x)(x+5) = NO</span>

3 0

3 years ago

Karen's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Karen $5.80 per pound, and type

Elina [12.6K]

Answer:

Step-by-step explanation:

A + B = 127

5.80A + 4.25B = 657.55

Solve with substitution.

5.80A + 4.25(127 − A) = 657.55

5.80A + 539.75 − 4.25A = 657.55

1.55A = 117.80

A = 76

8 0

3 years ago