If f(x) =

What is the value of f(4,7)? Explain and show your answers.

If f(x) = What is the value of f(4,7)? Explain and show your answers. We were...
Let f(x)=
if
,
if
if
a) What is the fomain of f(x)? Write in interval notation.
b) Determine the y-intercept of the function, if any. Make sure
to justify your answer.
c) Determine the x-intercepts of the function, if any. Justify
your answer.
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Prove, or give a counter example to disprove the following
statements.
a)
b)
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Let X be a banach space such that X= C([a,b]) where - ab+ with the sup
norm. Let x and f X. Show
that the non linear integral equation
u(x) = (sin
u(y) dy + f(x) ) has a solution u X. (the integral is
from a to b).
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Evaluate the flux F across the positively oriented surface
S
where
and S is the boundary of
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Calculate the work done by the vector field F(x,y)=4xy,
2x2
along a smooth, simple curve from point (3, −1) to point (4, 2)
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sin 0, cos 0
Name the quadrant in which the angle lies
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find the Laplace Transform of f(t) = t2 - 3t,
where f has a period 3, for 0
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Suppose that
is a bounded function with following Lower and Upper
Integrals:
and
a) Prove that for every
, there exists a partition
of
such that the difference between the upper and lower sums
satisfies
.
b) Furthermore, does there have to be a subdivision such that
. Either prove it or find a counterexample and show to the
contrary.
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A probability density function f of a continuous random variable
x satisfies all of the following conditions except
a)
b)
c) For any a,b with
, P()
=
d) The mean and variance of a probability density function f are
both finite
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Let
and consider the domain
(an open rectangle). Find the maximum of
on
as well as the
-value(s) at which
attains this maximum value.
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