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2 years ago

Which statement best explains the relationship

Mathematics

1 answer:

Tom [10]2 years ago

3 0

Answer:

They are parallel because their slopes are equal.

Step-by-step explanation:

See attached image.

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Find the Maclaurin series for the f(x)=xe^2x and find<br> itsradius of convergence.

snow_tiger [21]

Answer:

Step-by-step explanation:

Maclaurin series is a special form of Taylor series where a = 0,

$f(x)=\sum\limits^\infty_{n=0}\frac{f^{(n)}(0)(x-a)^n}{n!}=\sum\limits^\infty_{n=0}\frac{f^{(n)}(0)x^n}{n!}$

Hence,

$f\left(x\right)=f\left(0\right)+\frac{f^{'}\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots$

For $f(x)=xe^{2x}$ ,

$f\left(x\right)=0\cdot \:e^{2\cdot \:0}+\frac{\frac{d}{dx}\left(xe^{2x}\right)\left(0\right)}{1!}x+\frac{\frac{d^2}{dx^2}\left(xe^{2x}\right)\left(0\right)}{2!}x^2+\frac{\frac{d^3}{dx^3}\left(xe^{2x}\right)\left(0\right)}{3!}x^3+\ldots$

Where,

$0\cdot \:e^{2\cdot \:0}\quad :\quad 0\\\\\frac{d}{dx}\left(xe^{2x}\right)\left(0\right)\quad :\quad 1\\\\\frac{d^2}{dx^2}\left(xe^{2x}\right)\left(0\right)\quad :\quad 4\\\\\frac{d^3}{dx^3}\left(xe^{2x}\right)\left(0\right)\quad :\quad 12\\\\\frac{d^4}{dx^4}\left(xe^{2x}\right)\left(0\right)\quad :\quad 32\\\\\frac{d^5}{dx^5}\left(xe^{2x}\right)\left(0\right)\quad :\quad 80$

Thus,

$f\left(x\right)=0+\frac{1}{1!}x+\frac{4}{2!}x^2+\frac{12}{3!}x^3+\frac{32}{4!}x^4+\frac{80}{5!}x^5+\ldots=\\\\=x+2x^2+2x^3+\frac{4}{3}x^4+\frac{2}{3}x^5+\ldots$

3 0

3 years ago

What are the new coordinates of L' if the following image has a dilation of 1/2?

bulgar [2K]

B, divide it’s coordinates in half. -5/2 and -1/2.

3 0

2 years ago

Find the length of BC please

Doss [256]

Check the picture below.

make sure your calculator is in Degree mode.

7 0

3 years ago

Which table represents a non-linear function

siniylev [52]

The second table represents a non linear function because the x and y values when graphed do not line up along the line of best fit.

3 0

3 years ago

Andrew [12]

Answer:

Given the initial population of termites = 60

After 7 days the population of termites = 225

Step-by-step explanation:

We have given the initial termites and the population of termites after 7 days. Now we are required to find the exponential growth model that will help to predict the future population of termites.

We have, Y = Ca^x

When the value of x is zero then population (Y) is 60 termites.

Y = Ca^x

60 = Ca^x

Now, Y = 60a^x

At x = 7 days

Y = 225

225 = 60 a^7

a^7 = 225/60

a = 1.2078

Thus, final population will be, Y = 60(1.2078)^x

8 0

3 years ago