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2 years ago

Yankee with no brim yankee with no brim yankee with no brim yankee with no brim yankee with no brim

Mathematics

2 answers:

bonufazy [111]2 years ago

8 0

Answer:

Truly cursed.

adell [148]2 years ago

7 0

Answer:

woahh

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

Fiona spent $13.70 to travel across the city in a taxi. It cost her $3.25 to get the taxi and $2.75 each mile she traveled. Writ

Goryan [66]

$2.75m+3.25=13.70$

$2.75m=13.70-3.25\\\\2.75m=10.45\ \ \ /:2.75\\\\m=\frac{10.45}{2.75}\\\\m=\frac{1045}{275}\\\\m=3.8\ (miles)$

8 0

2 years ago

Read 2 more answers

When 5/8 of the books had been sold, there were only 309 books remaining. how many books were there originally?

Whitepunk [10]

There were 824 books originally

8 0

2 years ago

Solve 3x – ly= 11 and -2x – 4y=-26 by elimination

Ede4ka [16]

Answer:

(5, 4 )

Step-by-step explanation:

Given the 2 equations

3x - y = 11 → (1)

- 2x - 4y = - 26 → (2)

Multiplying (1) by - 4 and adding to (2) will eliminate the y- term

- 12x + 4y = - 44 → (3)

Add (2) and (3) term by term to eliminate y

- 14x + 0 = - 70

- 14x = - 70 ( divide both sides by - 14 )

x = 5

Substitute x = 5 into either of the 2 equations and solve for y

Substituting into (1)

3(5) - y = 11

15 - y = 11 ( subtract 15 from both sides )

- y = - 4 ( multiply both sides by - 1 )

y = 4

solution is (5, 4 )

7 0

2 years ago

Given A(-3, 6) and B(0, 6), what are the coordinates of point P that lies on segment AB, such that AP:PB = 2:1? A: (2, -2) B: (-

DerKrebs [107]

Answer:

(-1 1/2, 6)

Step-by-step explanation:

The mid point between A(-3,6) and B(0,6) represents the coordinates of point P, which is (x,y)

Hence,the coordinates, that is, AP: x = (-3 + 0)/2 = -3/2 = -1 1/2

also, BP: y = (6 + 6)/2 = 6

Therefore, the coordinates of point P = ( -1 1/2, 6)

7 0

2 years ago