Unformatted text preview: 1 Solutions 111 13.
. 14.
. 15.
16. 17. A is true since
satisﬁes the diﬀerential equation on each subinterval.
B is true since the left and right limits agree at
. C is not true since
.
18. A is true since
B is true since
. satisﬁes the diﬀerential equation on each subinterval.
. C is true since 19. A is true since
B is false since
since B is false. satisﬁes the diﬀerential equation on each subinterval.
while
. C is false 20. A is false since
on the interval does not satisfy the diﬀerential equation
. Since is false, B and C are necessarily false. 21. A is true since
B is true since satisﬁes the diﬀerential equation on each subinterval.
. C is false since
while
. D is false since C is false.
22. A is true since
satisﬁes the diﬀerential equation on each subinterval.
B is false since
while
.
C and D are false since B is false. You cannot have a continuous derivative
if the function is not continuous.
23. A is true since
B is true since satisﬁes the diﬀerential equation on each subinterval.
. C is true since
. D is true since .
24. A is true since
satisﬁes the diﬀerential equation on each subinterval. B is true since
. C is true since
. D is false since
.
25. The general solution of
on the interval
is found by using
the integrating factor
. The general solution is
and
the initial condition
gives
, so that
for
. Continuity of
at
will then give
, which will provide the initial condition for the next interval ...
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 Fall '08
 BELL,D
 Topology, Derivative, Continuous function

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