Ws 6.6 Improper Integrals Worksheet Page 6
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7Calculus Maximus
WS 6.6: Improper Integrals
13. (AP 2001-5) Let f be the function satisfying
f x
3
xf x
, for all real numbers x, with
f
1
4
.
and lim ( ) 0
f x
x
(a) Evaluate
3xf x dx
. Show the work that leads to your answer.
1
x with a step size of 0.5 , to approximate
(b) Use Euler’s method, starting at
1
f
2
.
dy
y
f x
(c) Write an expression for
by solving the differential equation
3
xy
with the intial
dx
.
condition
f
1
4
Page 6 of 7
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