Find a power series for the function, centered at
c.
f(x) =
3
2x − 1
, c = 2
f(x) =
∞
n = 0
Determine the interval of convergence. (Enter your answer using
interval notation.)
a) Find the Taylor series for sinh(x) (centered at x=0), for e^x
(centered at x=0) and hyperbolic sine and hyperbolic cosine.
b) same as a but cosh(x) instead
Use power series to find two linearly independent solutions
centered at the point x=0
1) y'' + 2y' - 2y = 0
2) 2x2y'' + x(x-1)y' - 2y = 0
please show work, thank you!
(a) Determine the Taylor Series centered at a = 1 for the
function f(x) = ln x.
(b) Determine the interval of convergence for this Taylor
Series.
(c) Determine the number n of terms required to estimate the
value of ln(2) to within Epsilon = 0.0001.
Can you please help me solve it step by step.
Solve the following differential equations using Taylor series
centered at 0. It’s enough to find the recurrence relation and the
first 3 terms of the series.
(a) y''− 2y' + y = 0
(b) y'' + xy' + 2y = 0
(c) (2 + x^2 )y'' − xy'+ 4y = 0