Please Prove the following, be clear and percise.
By removing sets with ever decreasing length, show...
Please Prove the following, be clear and percise.
By removing sets with ever decreasing length, show that we can
construct a "Cantor-like" set which has positive length. How large
can we make the length of this set?
Let A and B be sets. Prove the following please show in as much
detail as possible
i. A ⊆ B is and only if A U B = B
ii. A ⊆ B is and only if A ∩ B = A
iii. A ⊆ B is and only if A \ B = empty set
For each of the following sets, prove that thay are convex sets
or not. Also graph the sets.
a) ? 1= {(?1 , ?2 ): ?1 ^2 + ?2^2 ≥ 1}
b)?2 = {(?1 ,?2 ): ?1 ^2 + ?2^ 2 = 1}
c)?3 = {(?1 , ?2 ): ?1 ^2 + ?2 ^2 ≥ 1}
Prove the following statements!
1. If A and B are sets then
(a) |A ∪ B| = |A| + |B| − |A ∩ B| and
(b) |A × B| = |A||B|.
2. If the function f : A→B is
(a) injective then |A| ≤ |B|.
(b) surjective then |A| ≥ |B|.
3. For each part below, there is a function f : R→R that is
(a) injective and surjective.
(b) injective but not surjective.
(c) surjective but not injective.
(d)...
Numerical MethodsPlease show all steps with clear hand
writing.
Use numerical methods to Prove that the following equations have
at leat one solution in the given intervals.
(a) x − (ln x)3 = 0, [5, 7]
(b) 5x cos(πx) − 2x 2 + 3 = 0, [0, 2]
PLEASE SHOW CLEAR CALCULATION PLEASE
1. If a physician deposits $24,000 today into a mutual fund that
is expected to grow at an annual rate of 8%, what will be the value
of this investment:
what is the future value factor for each?
a. 3 years from now
b. 6 years from now
c. 9 years from now
d. 12 years from now
2. The Chief Financial Officer of a hospital needs to determine
the present value of $120,000 investment...
Question 1:
Part (A)
Prove the thin lens equation, geometrically.
Also show that the focal length of a curved mirror is 1/2 the
radius of curvature. DRAW good diagrams
Part (B).
White light is incident on a soap film (n = 1.33 and thickness =
800 nm) suspended in air. If the incident light makes a 45o angle
with the normal to the film, what visible wavelengths with be
constructively reflected?