vestirme4
2021-10-29
Answered

Find a power series representation for the function and determine the radius of convergence. $f\left(x\right)=\frac{x}{{(1+4x)}^{2}}$

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Faiza Fuller

Answered 2021-10-30
Author has **108** answers

Step 1

We will start with the power series of

We know that

Step 1 : Replace x with

Step 2

Differentiate both sides

Not that the sum in RHS is starting from

Divide both sides by

Step 3 : Multiply both sides by x

If you want you can start the sum from

asked 2021-05-14

Use the given graph off over the interval (0, 6) to find the following.

a) The open intervals on whichfis increasing. (Enter your answer using interval notation.)

b) The open intervals on whichfis decreasing. (Enter your answer using interval notation.)

c) The open intervals on whichfis concave upward. (Enter your answer using interval notation.)

d) The open intervals on whichfis concave downward. (Enter your answer using interval notation.)

e) The coordinates of the point of inflection.$(x,\text{}y)=$

a) The open intervals on whichfis increasing. (Enter your answer using interval notation.)

b) The open intervals on whichfis decreasing. (Enter your answer using interval notation.)

c) The open intervals on whichfis concave upward. (Enter your answer using interval notation.)

d) The open intervals on whichfis concave downward. (Enter your answer using interval notation.)

e) The coordinates of the point of inflection.

asked 2021-11-29

Eliminate the parameter $\theta$ in the following parametric equations

$x=a\mathrm{tan}\theta \text{}y=b\mathrm{sec}\theta$

asked 2021-12-06

Let P be the vector-valued function $P\left(t\right)=(\mathrm{sin}t+,\mathrm{cos}t)$ .

(a) What curve is traced by P? Draw a picture of this curve.

(b) Draw the vector${P}^{\prime}\left(\frac{\pi}{3}\right)$ at the point corresponding to $t=\frac{\pi}{3}$ on the picture you produced in part (a).

(c) Find a vector equation for the line tangent to the curve at$t=\frac{\pi}{3}$ .

(a) What curve is traced by P? Draw a picture of this curve.

(b) Draw the vector

(c) Find a vector equation for the line tangent to the curve at

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Solve the system of equations with elimination method and what is the type of solution?

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Polar coordinates of point P are given. Find all of its polar coordinates.

asked 2021-11-26

Which of the following vectorvalued functions represent the same graph?

a)$r\left(t\right)=(-3\mathrm{cos}t+1)i+(5\mathrm{sin}t+2)j+4k$

b)$r\left(t\right)=4i+(-3\mathrm{cos}t+1)j+(5\mathrm{sin}t+2)k$

c)$r\left(t\right)=(3\mathrm{cos}t-1)i+(-5\mathrm{sin}t-2)j+4k$

d)$r\left(t\right)=(-3\mathrm{cos}2t+1)i+(5\mathrm{sin}2t+2)j+4k$

a)

b)

c)

d)

asked 2021-09-04

Find the point(s) of intersection of the graphs of the equations.

A point of intersection of the graphs of two equations is a point that satisfies both the equations. You can find the point(s) of intersection of the graphs of the given equations by solving their equations simultaneously.

Solve the first equation for