Question

In the first two problems, find the first four non-zero terms of the Laurent series of the indicated functions.and Find the value of the 3rd term evaluated at ? = 2

1) ?(?) = 1 / ? for 6 < |? − 6|

2) ?(?) = 1 /? ^2 for 6 < |? + 6|

Answer #1

In the next two problems, find all Laurent series around the
indicated point and state the regions of convergence.and Find the
value of the 3rd term evaluated at ? = 2
3)?(?) = sin 1 /? , ?0 = 0 4) ?(?) = 1/ ? , ?0 = 3i

Find at least four non-zero terms in a power series expansion of
the solution to the initial value problem:
y'' + xy' + e^x y = 1-x^3
y(0) = 1, y'(0) = 0

Using the first four non-zero terms of the Taylor series
expansion of 12/x^4 , approximate the value of exp(0.01) and
calculate the error by comparing the obtained value with the actual
value of exp(0.01).

Find the first three non-Zero terms in the Taylor series
centered at 0 for the function.
f(x)=sin(3x)

Find the first 5 non-zero terms of power series
(1-x^2)y''-2xy'+2y =0

Find at least the first 3 non-zero terms of each series solution
for the particular solution and the two homogeneous solutions of
the differential equation:
y'' - sin(x)y = cos(x)

Find at least the first six non-zero terms of the general power
series solution, centered at the ordinary point ?=0, of the given
differential equation. Write your answer in standard form.
?''−?^2 ?'+?=0

Use the definition of a Taylor series to find the first four
nonzero terms of the series for f(x) centered at
the given value of a. (Enter your answers as a
comma-separated list.)
f(x) = 4/(1+x), a = 2
Use the definition of a Taylor series to find the first four
nonzero terms of the series for f(x) centered at
the given value of a. (Enter your answers as a
comma-separated list.)
f(x) = 3xe^x, a = 0

1- Use the definition of a Taylor series to find the first
four nonzero terms of the series for f(x) centered at the given
value of a. (Enter your answers as a comma-separated list.)
f(x) = 5 cos2(x), a = 0
2-
Use the definition of a Taylor series to find the first four
nonzero terms of the series for f(x)
centered at the given value of a.
(Enter your answers as a comma-separated list.)
f(x) = 9xex, ...

Find the first three non-zero terms in Taylor expansion of the
following function about the point indicated: y= ln(1 +
x2) about x = 0

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