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netineya [11]
3 years ago
5

What is the slope of the line that contains the points (-1,-1) and (3, 15)?

Mathematics
1 answer:
DanielleElmas [232]3 years ago
7 0

Answer:

its b

Step-by-step explanation:

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Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that
juin [17]

Answer:

The Taylor series of f(x) around the point a, can be written as:

f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....

Here we have:

f(x) = 4*cos(x)

a = 7*pi

then, let's calculate each part:

f(a) = 4*cos(7*pi) = -4

df/dx = -4*sin(x)

(df/dx)(a) = -4*sin(7*pi) = 0

(d^2f)/(dx^2) = -4*cos(x)

(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4

Here we already can see two things:

the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.

so we only will work with the even powers of the series:

f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....

So we can write it as:

f(x) = ∑fₙ

Such that the n-th term can written as:

fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}

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3 years ago
The side length of a square garden is 15 feet. Find the area of the garden in square feet.
viktelen [127]

To find the area multiply the length by the width.

The length and width of a square are the same.

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2 years ago
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The sum of 8 times a number and 3 equals 5
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8n+3=5
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N=.25

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Step-by-step explanation:

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Which expression is equivalent to the following?
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Step-by-step explanation:

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= (\sin^{2}x)^{2}  - (1 - \sin^{2}x)^{2}

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= 2\sin^{2}x - 1

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{ \sin }^{2} x =  \frac{1}{2} (1 -  \cos \: 2x)

for the last step.

PS. I love proving trigonometric identities!

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