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Mathematics

1 answer:

hodyreva [135]3 years ago

7 0

Answer:

The slope of function A is 2 times the slope of function B.

Step-by-step explanation:

In function A, every-time the input goes up 1 the output will also go up one. In function B, every time the input goes up by 1, the output goes up by two. Therefore, the slope of function A is 1 but the slope of function B is 1/2.

1/2*2=1

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James is x years old now and the sum of his age is and his brothers age is 10.

Vesnalui [34]

Answer:

1) James brother is 10-x years old

2) James was 3 years ago x-3 years old

3) James brother was 3 years ago 7-x years old

4) 3(x-3)=7-x

5) James is 4 years old, his brother is 6 years old

Step-by-step explanation:

3) 10 - x - 3 = 7 - x

5) 3* James age 3 years ago = James brothers age 3 years ago

<=> 3*(x-3) = 7-x

<=> 3x - 9 = 7 - x

<=> 4x = 16

<=> x = 4

5 0

3 years ago

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:

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