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3 years ago

Solve this equation by elimination method...

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

4 0

Answer:

x=2,y=-3

Step-by-step explanation:

detailed explanation showed in the image above

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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

3 x + 2 y = − 6. help me find the y and the x x y -4 0 0 –3

Maru [420]

Answer:

x = 0 and y = -3

Step-by-step explanation:

3 (0) = 0

2 (-3) = -6

So the answer would be x = 0 and y = -3

5 0

3 years ago

What is the sum of 4.2 × 10^5 and 5.3 × 10^5?

mojhsa [17]

C is the correct answer using scientific notation Hope this helps! :D

6 0

3 years ago

What is the domain of the relation?

Thepotemich [5.8K]

Answer: $-4$

Step-by-step explanation:

Domain: x-axis

Range: y-axis

The relation graph shows the points in which the domain is located. To find the Domain, go to the point in the x-axis (the horizontal line) and note the number where the point lies. For this question, the point on the left side of the graph lies on negative four ( $-4$ ), and on the right side, the point is on 6. Therefore, the domain of this relation is negative four is greater than/equal to x is less than/equal to six. It could also be written like this: $-4\leq x\leq 6$ .

Learn more: brainly.com/question/24574301

8 0

3 years ago

Urgent!! please help )):

alisha [4.7K]

The 16th term is: 53

Further explanation:

We have to find the general formula first

The general form is:

$a_n=a_1+(n-1)d\\Given\\a_1=8\\d=3\\Putting\ the\ values\ in\ the\ formula\\a_n=8+(n-1)(3)\\a_n=8+3n-3\\a_n=5+3n\\For\ 16th\ term, put\ n=16\\a_n=5+3(16)\\a_n=5+48\\a_n=53$

The 16th term is: 53

Keywords: Arithmetic sequence, Common Difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

4 0

3 years ago