Stepwise problems - Thu. 11:59pm
Power series: Radius and Interval
01
01
Link to originalPower series - radius and interval
Find the radius and interval of convergence for these power series:
(a)
(b) (c)
Power series as functions
02
01
Link to originalModifying geometric power series
Consider the geometric power series
for . For this problem, you should modify the series for
. (a) Write
as a power series centered at and determine its radius of convergence. (b) Write
as a power series centered at and determine its radius of convergence.
03
03
Link to originalFinding a power series
Find a power series representation for these functions:
(a)
(b)
Regular problems - Sun. 11:59pm
Series tests: strategy tips
04
01
Link to originalVarious limits, Part I
Find the limits. You may use
or or as appropriate. Braces indicate sequences.
- C = Convergent
- AC = Absolutely Convergent
- CC = Conditionally Convergent
- D = Divergent
C or D
C or D
AC, CC, or D
AC, CC, or D
05
02
Link to originalVarious limits, Part II
Find the limits. You may use
or or as appropriate. Braces indicate sequences.
- C = Convergent
- AC = Absolutely Convergent
- CC = Conditionally Convergent
- D = Divergent
C or D
C or D
AC, CC, or D
AC, CC, or D
Power series: Radius and Interval
06
02
Link to originalPower series - radius and interval
Find the radius and interval of convergence for these power series:
(a)
(b) (c)
07
03
Link to originalPower series - radius and interval
Find the radius and interval of convergence for these power series:
(a)
(b)
Power series as functions
08
02
Link to originalPower series of a derivative
Suppose that a function
has power series given by: The radius of convergence of this series is
. What is the power series of
and what is its radius of convergence?
09
04
Link to originalModifying and integrating a power series
(a) Modify the power series
for to obtain the power series for . (b) Now integrate this series to find the power series for
.