Number 
Question 
Answer 
See the work 
1.

Consider the function
Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. Also indicate the radius of convergence. Partial Sum:_______ Radius of Convergence:______

Partial sum:
Radius of convergence: 1

The work
Point Cost: 3 
2.

The function ƒ(x)= is represented as a power series
Find the first few coefficients in the power series
c0= ____ c1=____ c2=____ c3=____ c4=____
Find the radius of convergence R of the series.
R=_______

c0= 1 c1= see the work c2= see the work c3= 0 c4= 16 R= 1/2

The work
Point Cost: 4 
3.

Suppose that
Find the first few coefficients
c0= ____ c1=____ c2=____ c3=____ c4=____
Find the radius of convergence R of the series.
R=_______

c0= 0 c1= see the work c2= 1/4 c3= see the work c4= see the work R= 2

The work
Point Cost: 4 
4.

The function ƒ(x)= is represented as a power series
Find the first few coefficients in the power series
c0= ____ c1=____ c2=____ c3=____ c4=____
Find the radius of convergence R of the series.
R=_______

c0= 2 c1= 40 c2= 600 c3= 8000 c4= 100000 R= 1/10

The work
Point Cost: 4 
5.

consider the function ln(1+12x) Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. Partial Sum:______ Radius of convergence:_____

Sum: Radius: see the work 
The work
Point Cost: 4 
6.

The function ƒ(x)=7xln(1+2x) is represented as a power series
Find the following coefficients in the power series.
c0= ____ c1=____ c2=____ c3=____ c4=____
Find the radius of convergence R of the series. R=____

c0= 0 c1= 0 c2= see the work c3= see the work c4= 56/3 R= see the work

The work
Point Cost: 6 
7.

The function ƒ(x)= is represented as a power series.
Find the following coefficients in the power series.
c1= ____ c2=____ c3=____ c4=____ c5=____
Find the radius of convergence R of the series. R=____

c1= 0 c2= 7 c3= 56 c4= 336 c5= 1792 R= 1/4

The work
Point Cost: 4 
8.

Consider the function arctan(x/15). Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms.
Partial Sum:______ Radius of convergence:_____

Sum: see the work
R= 15

The work
Point Cost: 4 
9.

a) Consider the function arctan(x^2). Write a partial sum for the power series which represents this function consisting of the first 4 nonzero terms.
Partial Sum:______ Radius of convergence:_____
b) Use part a) to write the partial sum for the power series which represents ∫arctan(x^2)dx. Write the first 4 nonzero terms.
Partial Sum:______ Radius of convergence:_____
c) Use the partial sum for the power series ∫arctan(x^2)dx to approximate the integral .

a) Sum: see the work
R= 1
b) Sum:
R= 1
c) 0.11073

The work
Point Cost: 3 