Cram University
 
Username: Password:

Sign up (it's free!)   | |   forgot password?

 

Calc 2 8.7

 

<== Calculus 2
Number Question Answer
See the work

1.

 

The function ƒ(x)= sin(8x) has a Maclaurin series.
Find the first 4 nonzero terms in the series.

 

8*x-(8^3)/6 * x^3 + (8^5)/120 * x^5 - (8^7)/5040 * x^7
The work

Point Cost: 3

2.

 

 

 

 

 

 

 

Find the Maclaurin series of the function
ƒ(x)=coshx

c0=_____
c1=_____
c2=_____
c3=_____
c4=_____

radius of convergence
R=________

 

c0= 1
c1=0
c2= 1/2
c3= 0
c4= 1/24

R= ∞

The work

Point Cost: 1

3.

 

 

 

 

 

 

 

Find the Maclaurin series of the function
=4x^3-5x^2-5x+5

c0=_____
c1=_____
c2=_____
c3=_____
c4=_____

radius of convergence
R=________

 

c0= 3
c1= -8
c2= -3
c3= 3
c4=0
R= ∞
The work

Point Cost: 2

4.

 

 

 

 

 

The Taylor series for (x)=x^3 at -4 is

Find the first few coefficients.
c0=_____
c1=_____
c2=_____
c3=_____
c4=_____

 

c0= -64
c1= 48
c2= -12
c3= 1
c4= 0
The work

Point Cost: 3

5.

 

 

 

 

 

The Taylor series for (x)=e^x at a= 1 is
 
Find the first few coefficients.
c0=_____
c1=_____
c2=_____
c3=_____
c4=_____

 

c0= 2.71828182846
c1= 2.71828182846
c2= 1.35914091423
c3= 0.45304697141
c4= 0.1132617428525
The work

Point Cost: 3

6.

 

The function ƒ(x)=lnx has a Taylor series at
a=4. Find the first 4 nonzero terms in the series

 

ln(4)+1/4*(x-4)+(-1/2/4^2)*(x-4)^2+1/3/4^3 * (x-4)^3
The work

Point Cost: 3

7.

 

 

 

 

 

The Taylor series for ƒ(x)=cos(x) at a= π/4 is
 
Find the first few coefficients.
c0=_____
c1=_____
c2=_____
c3=_____
c4=_____

 

c0= 0.7071067811884
c1= -0.7071067811884
c2= -0.353553390593
c3= 0.117851130198
c4= 0.0294627825494
The work

Point Cost: 1

8.

 

The function (x)=x^-3 has a Taylor series at
a=1. Find the first 4 nonzero terms in the series

 

1-2*(x-1)+2*(2+1)*(x-1)^2/2-2*(2+1)(2+2) * (x-1)^3/6
The work

Point Cost: 3

9.

 

 

 

 

 

 

Find the Maclaurin series of the function
(x)=(4x^2)sin(3x)

c0= _____
c1= _____
c2= _____
c3=_____
c4=_____
c5=_____
c6=_____
c7=_____

 

c0= 0
c1= 0
c2= 0
c3= 12
c4= 0
c5= see the work
c6= 0
c7= see the work
The work

Point Cost: 4

10.

 

 

 

 

 

 

Find the Maclaurin series of the function
(x)=(9x^2)e^(-10x)

c0=_____
c1=_____
c2=_____
c3=_____
c4=_____

 

c0= 0
c1= 6
c2= -18
c3= 27
c4= -27
The work

Point Cost: 3

11.

 

 

 

 

 

 

 

Use the binomial series to expand the function

f(x)=1/(1-5x)^(1/4)

as a power series

\sum_{n=0}^\infty c_n  x^n

Compute the following coefficients.

c0=_____
c1=_____
c2=_____
c3=_____
c4=_____
c0= 1
c1= 1.25
c2= 3.90625
c3= 14.6484375
c4= 59.50927734375

 

The work

Point Cost: 3

12.

 

 

 

 

 

 

 

Consider the function

(e^(7x)-1)/x
a)Write the first 3 non zero terms of the
MacLaurin series for the function.

b)Use part a) to write the first 3 non zero
terms of the MacLaurin series for

int(e^(7x)-1)/x

 

a) 7+24.5x+57.1667x^{2}

b) 7x+12.25x^{2}+19.0556x^{3}

The work

Point Cost: 3

13.

 

 

 

 

Assume that sin(x) equals its Maclaurin series for all x.
Use the first two terms of the Maclaurin series for

sin(5x^2)

to evaluate the integral

a= 0.76<br /> b= 0 sin(5x^2)dx

 

0.184631
The work

Point Cost: 2

14.

 

 

 

 

Evaluate

Use power series

 

1/48
The work

Point Cost: 2

15.

 

 

 

Evaluate

Use power series

-9/14
The work

Point Cost: 2

16.

 

 

 

Use the binomial series to expand the function

f(x)=1/(2+x)^3

as a power series

\sum_{n=0}^\infty c_n  x^n

Compute the following coefficients.

c0=_____
c1=_____
c2=_____
c3=_____
c4=_____
c0=0.125
c1=-0.1875
c2=0.1875
c3=-0.15625
c4=0.1171875
The work

Point Cost: 3