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2 years ago

Can somebody please help me

Mathematics

2 answers:

sertanlavr [38]2 years ago

7 0

A is the right answer

Natalija [7]2 years ago

3 0

A is the correct answer

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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

Solve the equation. n+34=14

wlad13 [49]

Answer:

n = -20

Step-by-step explanation:

Subtract 34 on both sides of the equation:

n = 14 - 34

n = -20

Hope this helps!

4 0

3 years ago

Read 2 more answers

A fraction has a fraction in the numerater , denominator,or both

Arlecino [84]

Fraction has fraction in both

6 0

3 years ago

You get a part-time job earning $8.60/hr. Tips are $3.25/hr on average. Deductions are FICA (7.65%), federal tax withholding (11

adelina 88 [10]

Answer:

Gross Base pay is equals to $129

Step-by-step explanation:

Gross base pay can be defined as the pay per hour which has been discussed and finalized by the employer and employee at the time of job offering. It is the minimum amount of pay the employee is to receive. The tips, bonuses, allowances are not considered in the Gross base pay. Moreover, it is the basic pay an employee gets before any kind of tax deductions..

Gross base pay can easily be calculated by multiplying the pay per hour with the number of hours worked.

Pay per hour = $8.60

Numbers of hours worked = 15

Gross Base Pay = 8.60×15 = $129

3 0

3 years ago

A rectangle has a width represented by the expression 2y and a length represented by 12y - 5. which expression represents the ar

docker41 [41]

Correct option is B. Area of rectangle is $24y^{2} - 10 y$

We know that area of rectangle = Length × Width

We are given,

Length = 12y - 5

Width = 2y

So, area of rectangle = (12y - 5) × (2y)

= $(12y - 5)$ × $(2y)$

= (12y × 2y) - (5 × 2y)

= $24 y^{2} - 10 y$

<h3>What are algebraic equations?</h3>

An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. Also Check: Algebraic Expressions. In simple words, equations mean equality i.e. the equal sign.

To learn more about algebraic equations from the given link

brainly.com/question/11516438

#SPJ4

6 0

1 year ago