Calculus II Homework Problem

• Apr 3rd 2010, 01:06 PM
colonelone
Calculus II Homework Problem
I ran across a problem in my Calculus II homework that I could use some help on.

a)
Consider the function f(x)=e^x
Find the equation of a line p(x)=A+Bx with the property p(0)=f(0), and p ' (0)=f ' (0)
Find p by setting up and solving these equations for A and B

b)
Next find the approximating quadratic, p2(x) = A + Bx + Cx2 such that,
p2(0) = f(0); p2 ' (0) = f ' (0); and P2 " (0) = f " (0):
by solving the equations for A, B, and C.

c)
Set up and find p4(x) explicitly for f(x)=e^x by extending the conditions as in the problems above

d)
Write your polynomials involving "n!". Discuss how you could guess p3 and p5, as well as why "n!" keeps showing up.

• Apr 3rd 2010, 01:27 PM
chiph588@
Quote:

Originally Posted by colonelone
I ran across a problem in my Calculus II homework that I could use some help on.

a)
Consider the function f(x)=e^x
Find the equation of a line p(x)=A+Bx with the property p(0)=f(0), and p ' (0)=f ' (0)
Find p by setting up and solving these equations for A and B

p(0)=A+B*0 = A = f(0)
p'(x)=B, so p'(0)=B=f'(0)

And we know how to find f(0) and f'(0), right?
• Apr 3rd 2010, 02:00 PM
colonelone
Quote:

Originally Posted by chiph588@
p(0)=A+B*0 = A = f(0)
p'(x)=B, so p'(0)=B=f'(0)

And we know how to find f(0) and f'(0), right?

F(0) would just be e^0 or 1, and f'(0) would be e^0 or 1 as well. So A and B are each 1?
• Apr 3rd 2010, 03:49 PM
chiph588@
Quote:

Originally Posted by colonelone
F(0) would just be e^0 or 1, and f'(0) would be e^0 or 1 as well. So A and B are each 1?

correct.