Question

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).

Answer #1

Find the first four terms in the Taylor series expansion of the
solution to
y′(x) = 2xy(x)−x3, y(0) = 1.

Find the first four nonzero terms in the Taylor series expansion
of the solution of (x 2−2x)y 00+2y = 0, y(1) = −1, y 0 (1) = 3
about x0 = 1.

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

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

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 Taylor series of e^x about x = 3, find the first three
terms of Taylor series and the error in terms of h for
e^(3−2h).

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, ...

definition of a Taylor series to find the first 4 nonzero terms
of the power series for f(x) centered at the given value of a.
f(x)=3cuberoot(x^4) , a = 8

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|

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