2 years ago

What is 2/3 + 2/4, 1/3 + 3/4, 1/2 + 3/5 and, 1/2 + 3/4?

Mathematics

1 answer:

zalisa [80]2 years ago

4 0

1 and 1/6

1 and 1/12

1 and 1/10

1 and 1/4

Hope this helps! a

May I please get brainliest? :D

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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,

$\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

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3 years ago

Erin is comparing two rental car companies for an upcoming trip. The function

liberstina [14]

Answer:

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Step-by-step explanation:

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2 years ago

What is 3/4 divided by 1/8? Show/explain your reasoning. (I need this answer ASAP please.)

irga5000 [103]

Answer:

3/4 divided by 1/8 Is 6

Step-by-step explanation:

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2 years ago

If you multiply a whole number by a fraction what will be true about the answer

Rudiy27

Answer:

The true statement is that the answer will be a fraction.

Step-by-step explanation:

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2 years ago

The sum of 4 consecutive integers is 40 what is the third number in this sequence?

Dmitry [639]

Let's represent the numbers by : x, x+1, x+2, x+3
x+x+1+x+2+x+3=40 The third number in the sequence is x+2
4x+6=40 8.5+2=10.5
4x+6-6=40-6 Therefore the third number in the sequence is
4x=34 10.5
4x/4=34/4
x=8.5

3 0

3 years ago