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2 years ago

Explain how you could use a number line to show that -4 + 3 and 3 + (-4) have the same value

1 answer:

iogann1982 [59]2 years ago

6 0

Find (-4) on the number line and move 3 to the right. You will end up at (-1).

Find (3) on the number line and move 4 to the left. You will end up at the same value of (-1).

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Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

aliya0001 [1]

Answer:

$f(x)=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}$

Step-by-step explanation:

The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

$f(x)=f(0)+f^{\prime}(0)x+f^{\prime \prime}(0)\dfrac{x^2}{2!}+ ...+f^{(n)}(0)\dfrac{x^n}{n!}+...$

We first compute the n-th derivative of $f(x)=\ln(1+2x)$ , note that

$f^{\prime}(x)= 2 \cdot (1+2x)^{-1}\\f^{\prime \prime}(x)= 2^2\cdot (-1) \cdot (1+2x)^{-2}\\f^{\prime \prime}(x)= 2^3\cdot (-1)^2\cdot 2 \cdot (1+2x)^{-3}\\...\\\\f^{n}(x)= 2^n\cdot (-1)^{(n-1)}\cdot (n-1)! \cdot (1+2x)^{-n}\\$

Now, if we compute the n-th derivative at 0 we get

$f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!$

and so the Maclaurin series for f(x)=ln(1+2x) is given by

$f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2 \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}$

3 0

2 years ago

I need help, i have a quiz on it soon.

Nezavi [6.7K]

Answer:

okay

Step-by-step explanation:

complementary angles are angles that add up to 90 degrees

so what you would do is take each number that you have and subtract it from 90

In the first one you would

1. take 90-80

2. you get your answer of 10!

i hope this helps :)

8 0

2 years ago

Help... pls ASAP Fill in the blanks

Elis [28]

Answer:

I got this! Basically, the instructions say 12 gallons per 3 minutes. So you plug in the 12/3 to find the ratio of how many gallons per 1 minute.

Step-by-step explanation:

So, for the chart you just mulitply and evauluate

Time (min) | 2 | 3 | 4 | 5 | 6 |

Water used (gal) | 8 | 12 | 16 | 20 | 24 |

8 0

2 years ago

What's the reciprocal of 1/7

Nonamiya [84]

The answer is 7/1, when you want to know a reciprocal, all you do to the fraction is flip it around. Hope this Helps!

8 0

2 years ago

Read 2 more answers

If you are given a part-to-whole ratio, can you write part-to-part ratio? Explain

stealth61 [152]

There are 2 types of ratios: Part-to-Wholes, and Part-to-Part ratios.

Part-to-part ratios show the relationship between the two groups.

Lets say theres 10 fruits in a fruit bowl.

If you have 3 apples, and 7 oranges, then the ratio is 3:7 as the part-to-part ratio. But the part-to-whole ratio would be either 3:10 ( for apples) or 7:10 (for oranges)

8 0

3 years ago