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Calc 2 8.6

 

<== Calculus 2
Number Question Answer
See the work

1.

 

 

 

 

Consider the function

1/(1-x^5)
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: 1+x^5+x^(2*5)+x^(3*5)+x^(4*5)   

Radius of convergence: 1

The work

Point Cost: 3

2.

 

 

 

 

 

 

 

 

The function ƒ(x)=1/(1+4x^2) is represented as a power series

f(x)=cnx^n

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)==2/(1-10x)^2 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: 12(x-6x^2+48x^3-432x^4+4147.2x^5)
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)=(7x^2)/(1-4x)^2 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 \int_0^{0.7} \arctan( x^2) dx.

a) Sum: see the work
 R= 1

b) Sum:

    R= 1

c) 0.11073

The work

Point Cost: 3