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3 years ago

What information do you need to accurately describe a translation

Mathematics

1 answer:

Gelneren [198K]3 years ago

5 0

Answer:

make sure you have a good understanding of the subject you are translating, and that the translation is for that subject

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If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.

Pie

Given that $f^{(n)}(0)=(n+1)!$ , we have for $f(x)$ the Taylor series expansion about 0 as

$f(x)=\displaystyle\sum_{n=0}^\infty\frac{(n+1)!}{n!}x^n=\sum_{n=0}^\infty(n+1)x^n$

Replace $n+1$ with $n$ , so that the series is equivalent to

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}$

and notice that

$\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}$

Recall that for $|x|$ , we have

$\displaystyle\sum_{n=0}^\infty x^n=\frac1{1-x}$

which means

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}=\frac{\mathrm d}{\mathrm dx}\frac1{1-x}$
$\implies f(x)=\dfrac1{(1-x)^2}$

5 0

3 years ago

What variable do we use for slope? A.x B.y C.m D.b

Nady [450]

Answer:

y we use y

Step-by-step explanation:

6 0

3 years ago

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Please help I dont understand

riadik2000 [5.3K]

Answer:

2.1

Step-by-step explanation:

By the Law of Cosines,

a² = 5² + 6² - 2(5)(6)cos(20°)

a = sqrt(5² + 6² - 2(5)(6)cos(20°)), which is about 2.1

7 0

2 years ago

A data set includes the following grades: 98, 94, 93, 82, 61, 80. Suppose that 61 is removed from the data. How is the median af

puteri [66]

Answer:

<u>If we remove 61 from the data set, the median changes from 87.5 to 93.</u>

Step-by-step explanation:

1. Let's calculate the median of the original data set:

Median = (3rd term + 4th term)/2 because the number of terms are even and our median mark is the average of the two middle marks, in this case, 82 and 93.

Median = (82 + 93)/2

Median = 87.5

2. Let's calculate the median of the data set removing 61:

Median = 3rd term because our median mark is the middle mark, in this case, 93. It is the middle mark because there are 2 scores before it (80 and 82) and 2 scores (94 and 98) after it.

Median = 93

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3 years ago

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Rhea is solving a math puzzle. To find the solution of the puzzle, she must find the product of two numbers. The first number is

SashulF [63]

Answer:

I got P(x) = 2x^2 + 28x - 414

Step-by-step explanation:

I hope this helps you!! Have a lovely day

3 0

3 years ago

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