Show that if
is the cycle
. Give examples. What does this say for 2-cycles?
Show that if is the cycle . Give examples. What does this say for 2-cycles? We...
Give examples, if possible, of the following.
i) A set
with a supremum but no maximum.
ii) A decreasing sequence
so that
does not exist
iii) An increasing sequence
so that
does not exist.
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Give three examples for Rolle's Theorem: For the
first, define f : [0, 1] R such that
condition 1 does not hold, condition 2 does hold, condition 3 does
hold, and f'(c)0 for every c
(0,1). For the second example, make sure only condition
2 does not hold and the conclusion do not hold. For the third
example, do the same with condition 3.
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Let
be an arbitrary function and A
X.
i) Show that A
ii) Give an example to show that in general A =
.
iii) Show that, if
is injective, then A =
iv) Show that, if X and Y are modules;
is a homomorphism of modules and A is a submodule of X such that
ker,
then we also have A =
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Let
and define
by .
(a) Show is one-to-one
(b) What is the formula for
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Suppose is a finite dimensional vector space. For hyperplanes in say they are linearly independent provided the corresponding linear subspaces in are linearly independent. Set and show that are linearly independent if and only if . (Hint: Write for and consider by ). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageimnH...
For what values of
and
does the equality
hold true?
= and
=
At these values, the resulting vector is
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Demand for novels is given by D(p)=50.0−1.0p, and the supply
function is S(p)=1.0p.
Give all answers to one decimal.
A) What is the equilibrium price for
novels? $
B) What is the equilibrium quantity?
C) Suppose a $1 per-unit tax is imposed on buyers of novels.
Find the equilibrium price buyers pay, the price sellers receive,
and the quantity with the tax.
Buyers pay $ .
Sellers receive $ .
novels are sold.
D) Would the answer to Part 2 be different...
Let
be a sequence of independent random variables with
and
. Show that
in probability,
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Which of the following alternating series converge? Please show
work. Thank you!
1.
2.
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For both examples:
* show the complete hydrogen reaction (addition of Hydrogen)
*Draw the structure of the product (for both)
* What is the name of the product? (for both)
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