Finding Intervals of Convergence In Exercises 49-52, find the intervals of convergence of (a). f ( x ) (b) f ' ( x ) , (c) f " ( x ) . and (d) ∫ f ( x ) d x . . (Be sure to include a check for convergence at the endpoints of the intervals.) f ( x ) = ∑ n = 1 ∞ ( − 1 ) n + 1 ( x − 1 ) n + 1 n + 1
Finding Intervals of Convergence In Exercises 49-52, find the intervals of convergence of (a). f ( x ) (b) f ' ( x ) , (c) f " ( x ) . and (d) ∫ f ( x ) d x . . (Be sure to include a check for convergence at the endpoints of the intervals.) f ( x ) = ∑ n = 1 ∞ ( − 1 ) n + 1 ( x − 1 ) n + 1 n + 1
Solution Summary: The author calculates the Interval of convergence of la, b, and c.
Finding Intervals of Convergence In Exercises 49-52, find the intervals of convergence of (a).
f
(
x
)
(b)
f
'
(
x
)
, (c)
f
"
(
x
)
. and (d)
∫
f
(
x
)
d
x
.
. (Be sure to include a check for convergence at the endpoints of the intervals.)
f
(
x
)
=
∑
n
=
1
∞
(
−
1
)
n
+
1
(
x
−
1
)
n
+
1
n
+
1
Derive difference formulas for the first, second, and third
derivatives of a function f at a point x, using interpolation at
f(x-h), f(x), f(x + h), and f(x + 2h) Find the order of convergence
for all the approximations
Find the intervals of convergence of f(x), f '(x), f"(x), and f(x) dx. Include a check for convergence at the endpoints of the interval. (Enter your answer using interval notation.)
(-1)" + 1(x – 2)"
Σ
f(x) =
n = 1
(a)
n2"
f(x)
(b)
f'(x)
(c)
f"(x)
f(x) dx
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