Use (15.2) repeatedly to show that J 1 ( x ) = x − 1 x d d x J 0 ( x ) , J 2 ( x ) = x 2 − 1 x d d x 2 J 0 ( x ) , and, in general, J n ( x ) = x n − 1 x d d x n J 0 ( x ) .
Use (15.2) repeatedly to show that J 1 ( x ) = x − 1 x d d x J 0 ( x ) , J 2 ( x ) = x 2 − 1 x d d x 2 J 0 ( x ) , and, in general, J n ( x ) = x n − 1 x d d x n J 0 ( x ) .
Use (15.2) repeatedly to show that
J
1
(
x
)
=
x
−
1
x
d
d
x
J
0
(
x
)
,
J
2
(
x
)
=
x
2
−
1
x
d
d
x
2
J
0
(
x
)
, and, in general,
J
n
(
x
)
=
x
n
−
1
x
d
d
x
n
J
0
(
x
)
.
Calculate R3 and L3 for f(x) = x2-8x+2 over [1,4] .
Suppose that f(z) = x² - y² - 2y + i(2x - 2xy), where z = x+iy. Write f(z) in terms of
z, and simplify the result.
(Hint: You may prove and use the expressions x =
and y =
2. Determine the inverse of each function, then state its domain and range.
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