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2 years ago

Which relation defined by mapping diagram is a function

Mathematics

1 answer:

liq [111]2 years ago

3 0

Hello! A diagram is a function, when the domain of a number only has one range. By looking at this graph, A is eliminated, because 1 has more than one range. Exact same thing with C. The only diagram that shows a function is B, because no domain has more than one range. All of the numbers have one range, and that diagram makes a function. The answer is B.

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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

What angle relationship Describes angles CBE and DEB? I need answered back quick

Usimov [2.4K]

same-side interior angles

3 0

2 years ago

I like Pho shudbixbuebxubeuxbuebxube

pentagon [3]

me to so we don’t know how long it is for you

7 0

2 years ago

Read 2 more answers

In your pattern which shape covers more of the plane blue rhombus red trapezoid or green triangles? Explain how you know.

mixas84 [53]

Answer:

Which shapes cover more of the plane" means that we are comparing the areas covered by the different types of shapes. In these patterns, two triangles match up to one rhombus, and three triangles match up to one trapezoid.

In both Pattern A and Pattern B, the first hexagonal part is made up of 7 triangles, 4 rhombuses, and 3 trapezoids.

The first hexagonal part is repeated across the pattern, so whichever type of shape covers the most area of this first part also covers the most area in the whole pattern.

<em>hope it helps</em>

3 0

2 years ago

How do I solve this and what is the answer?

DanielleElmas [232]

Answer:

You use PEMDAS.

Step-by-step explanation:

If you dont know what that is, its the process used for long multistep equations like that : Parenthesis, Exponents, Multiplication, Division, Addition, then Subtraction. You solve all of those in order (if they are included in the problem). So for this you would solve one side of the inequality sign first using this order, then the other side and BAM! you've solved this problem.

8 0

2 years ago