At an effective annual interest rate of
,
, the following two sets of payments have the same present
value:
(i) A payment of 64 immediately and another payment of 64 at the end of 1 year
(ii) A payment of 125 at the end of 3 years and another payment of 125 at the end of four years
Compute the effective rate of discount
equivalent to
when
we assumed i=20% but value of 1st set equation is lower than value
of 2nd set. Therefore, we assumed (i) higher than 20 so as to
reduce the value of 2nd set. This results, value of both equations
become equal.
At an effective annual interest rate of , , the following two sets of payments have...
Prove, or give a counter example to disprove the following
statements.
a)
b)
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Solve the harmonic oscillator motion for initial conditions x(0)
= 0, V(0) = V0 in the case of (a) underdamped
(b) overdamped
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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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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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COMPLEX ANALYSIS:
Solve the integral
where
and
.
Please use JORDAN'S LEMMA and show all of your work.
Thank you!
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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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Define
a prime number,
a finite group,
as a Sylow
-subgroup of
.
Assume there exists
a proper subgroup of
where
, i.e. the normaliser of
in
is a subgroup of
.
Prove that
isn't normal in
.
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Use Snell's Law to solve for the critical angle
within the terms of and
.
= 90
degrees
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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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