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2 years ago

What is greatest to least 1.001,1.1,1.403,1.078

Mathematics

2 answers:

RSB [31]2 years ago

7 0

1.403, 1.1, 1.078, 1.001

Vlad [161]2 years ago

4 0

From greatest to least, 1.403, 1.1, 1.078, 1.001 This can be seen easier by putting zeros at the end of some numbers, but you don't have to. Example: 1.403, 1.100, 1.078, 1.001

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Use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x) = sin x, c = 3π/4

anyanavicka [17]

Answer:

$\sin(x) = \sum\limit^{\infty}_{n = 0} \frac{1}{\sqrt 2}\frac{(-1)^{n(n+1)/2}}{n!}(x - \frac{3\pi}{4})^n$

Step-by-step explanation:

Given

$f(x) = \sin x\\$

$c = \frac{3\pi}{4}$

Required

Find the Taylor series

The Taylor series of a function is defines as:

$f(x) = f(c) + f'(c)(x -c) + \frac{f"(c)}{2!}(x-c)^2 + \frac{f"'(c)}{3!}(x-c)^3 + ........ + \frac{f*n(c)}{n!}(x-c)^n$

We have:

$c = \frac{3\pi}{4}$

$f(x) = \sin x\\$

$f(c) = \sin(c)$

$f(c) = \sin(\frac{3\pi}{4})$

This gives:

$f(c) = \frac{1}{\sqrt 2}$

We have:

$f(c) = \sin(\frac{3\pi}{4})$

Differentiate

$f'(c) = \cos(\frac{3\pi}{4})$

This gives:

$f'(c) = -\frac{1}{\sqrt 2}$

We have:

$f'(c) = \cos(\frac{3\pi}{4})$

Differentiate

$f"(c) = -\sin(\frac{3\pi}{4})$

This gives:

$f"(c) = -\frac{1}{\sqrt 2}$

We have:

$f"(c) = -\sin(\frac{3\pi}{4})$

Differentiate

$f"'(c) = -\cos(\frac{3\pi}{4})$

This gives:

$f"'(c) = - * -\frac{1}{\sqrt 2}$

$f"'(c) = \frac{1}{\sqrt 2}$

So, we have:

$f(c) = \frac{1}{\sqrt 2}$

$f'(c) = -\frac{1}{\sqrt 2}$

$f"(c) = -\frac{1}{\sqrt 2}$

$f"'(c) = \frac{1}{\sqrt 2}$

$f(x) = f(c) + f'(c)(x -c) + \frac{f"(c)}{2!}(x-c)^2 + \frac{f"'(c)}{3!}(x-c)^3 + ........ + \frac{f*n(c)}{n!}(x-c)^n$

becomes

$f(x) = \frac{1}{\sqrt 2} - \frac{1}{\sqrt 2}(x - \frac{3\pi}{4}) -\frac{1/\sqrt 2}{2!}(x - \frac{3\pi}{4})^2 +\frac{1/\sqrt 2}{3!}(x - \frac{3\pi}{4})^3 + ... +\frac{f^n(c)}{n!}(x - \frac{3\pi}{4})^n$

Rewrite as:

$f(x) = \frac{1}{\sqrt 2} + \frac{(-1)}{\sqrt 2}(x - \frac{3\pi}{4}) +\frac{(-1)/\sqrt 2}{2!}(x - \frac{3\pi}{4})^2 +\frac{(-1)^2/\sqrt 2}{3!}(x - \frac{3\pi}{4})^3 + ... +\frac{f^n(c)}{n!}(x - \frac{3\pi}{4})^n$

Generally, the expression becomes

$f(x) = \sum\limit^{\infty}_{n = 0} \frac{1}{\sqrt 2}\frac{(-1)^{n(n+1)/2}}{n!}(x - \frac{3\pi}{4})^n$

Hence:

$\sin(x) = \sum\limit^{\infty}_{n = 0} \frac{1}{\sqrt 2}\frac{(-1)^{n(n+1)/2}}{n!}(x - \frac{3\pi}{4})^n$

3 0

2 years ago

What additional piece of information must be known in order to calculate the volume of the cylinder below?

Brilliant_brown [7]

Answer:

Step-by-step explanation:

the formula is V = πr2h

pie times radius to the second power times hight

6 0

2 years ago

Asap asap asap asap asap asap asap

IrinaK [193]

Answer:

4.8

Step-by-step explanation:

JK is twice as long as LM, so is 4.8 units long.

"Similar" means the sides of one figure have the same ratio as the corresponding sides of the other figure. We see that AB = 2×CD. JK corresponds to AB, and LM corresponds to CD.

We could bother to calculate that sides of JKLM are 1.2 times as long as the corresponding sides of ABCD, but that is not necessary. We only need to find a convenient ratio between the side we want and some other known side. I like a ratio of 2, because it is easy to double a number. We find AB=2CD, so JK=2LM=2×2.4 = 4.8.

8 0

2 years ago

Read 2 more answers

9: Part A The diameter of a circle is 63 centimeters. Find its circumference. Use π=3.14. A 31.5 centimeters B 98.91 centime

BaLLatris [955]

Part A:
The circumference of the circle is 197.92.

Explanation:
The formula for circumference of a circle is C=2 πr. If you insert the numbers, it would be C=2 x 3.14 x 31.5. Hence, the answer is 197.92.

Part B:
The area is 3117.25 square cm.

Explanation:
The formula for area of a circle is A= πr ². Inserting the numbers, it is A=3.14 x 31.5 ². Therefore the answer is 3117.25 cm ².

6 0

3 years ago

What is the Mean , Median , Mode , Range for <br>9,6,7,5,3

-Dominant- [34]

Answer:

the mean is 6

the median is 6

the mode there is none

the range is 6.

8 0

2 years ago

Read 2 more answers