Question

Let f have a power series representation, S. Suppose that f(0)=1, f’(0)=3, f’’(0)=2 and f’’’(0)=5.

a. If the above is the only information we have, to what degree
of accuracy can we estimate f(1)?

b. If, in addition to the above information, we know that S
converges on the interval [-2,2] and that |f’’’’(x)|< 11 on that
interval, then to what degree of accuracy can we estimate
f(1)?

Answer #1

Suppose R>0. Which of the following statements might be true
about a power series centered about the point x=a
a) The series converges for all x>a
b) The series converges on the interval (a,R)
c)The series converges on the interval [a,R)
d) The series converges only at x=a+R
e) All of the above
f) None of the above

Suppose R>0. Which of the following statements might be true
about a power series centered about the point x=a
a) The series converges for all x>a
b) The series converges on the interval (a,R)
c)The series converges on the interval [a,R)
d) The series converges only at x=a+R
e) All of the above
f) None of the above

find the power series representation centered at a=0 of
a.) f(x) = x/(5+7x)
b.) f(x) = x^2 sin(3x)

Find a power series representation for the function; determine
the interval of convergence. f(X) = (3x^2)/(5x+1)

find the power series representation for the function f(x) = x /
(1-x)^2

Find a power series representation for the function.
f(x) = ln(5 − x)
f(x) = ln(5) +
∞
(−1)nn(x5)n
n = 0
Determine the radius of convergence, R.
R =

Find a power series representation for the function.
f(x)=x^3/(x-8)^2
f(x)=SIGMA n=0 to infinity
Determine the radius of convergence
Use a Maclaurin series in this table to obtain the Maclaurin
series for the given function
f(x)=xcos(2x)

let
f(x)=ln(1+2x)
a. find the taylor series expansion of f(x) with center at
x=0
b. determine the radius of convergence of this power
series
c. discuss if it is appropriate to use power series
representation of f(x) to predict the valuesof f(x) at x= 0.1, 0.9,
1.5. justify your answe

Find a power series representation for the function and
determine the radius of convergence.
1) f(x)=x^3/(x-2)^2
2) f(x)=arctan(x/3)

Find the power series representation for the function: f(x) =
x2 / (1+2x)2 Determine the radius of
convergence.

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