cardinal numbers show the following: (a) cdo =C (Hint: We know that 240 = C, where...
1. (10 points) We want to compare the numbers 3 and -6. Using 4-bit signed 2's complement numbers, show how we can use the process of binary addition to calculate a result that will tell us how these two numbers compare. (Just show the calculation here. The next part will be the interpretation of the result.) Now briefly explain how this result can be interpreted by a hardware circuit to indicate how the two numbers compare. (You don't need to...
Consider the following binomial
tree. The numbers in squares are stock prices. The numbers in
circles will be option prices (# numbers are the exercise numbers
to answer your calculation).
Today, the stock is at 100 and can go up and down over the next
week, and then again up and down from there. We are pricing a call
struck at 93.
Use the computed q to sweep back through the tree to fill the
call values in circles. For...
17-26
true or false questions
17. The smallest positive real number is c, where c = card(0,1). 18. To show that two sets A and B are equal, show that x A and x B. 19. If (vx)P(e) is false, then P(x) is never true for that domain. 20. If R is a relation on A and if (a, a) is true for some a in A, then R is reflexive. 21. If f:A → B is a function, then...
show detailed work in each problem
For the following exercises, find the local and/or absolute maxima for the functions over the specified domain. 128. y = 4 sin - 3 cose over [0, 21) For the following exercises, show there is no c such that f(1)-f(-1) = f'(c)(2). Explain why the Mean Value Theorem does not apply over the interval [-1, 1). 168. f For the following exercises, determine a. intervals where f is increasing or decreasing, b. local minima...
Suppose we have a quantum system with N eigenstates. Then we know the eigenstates can be expressed as vectors, and operators can be represented by N × N matrices (a) Prove that (A)(A)where At is the transpose conjugate of matrix A. Here, A is not required to be Hermitian operator (Hint: express A and) in matrix and vector form. Use matrix calculation to show that (Αψ|U) is the same as 1Atlp.) (b) Prove that (ΑΒψ|U)-(ψ1BtAtlp). Á and B are not...
Algebra We know that matrix multiplication is not commutative: if A and B are square matrices of the same size, AB and BA are usually different We say that A and B commute if it so happens that AB BA. Determine all numbers a, b, e, d, such that the matrix com- mutes with both Calculus An object with mass m is dragged along a horizontal plane by a force acting along a rope attached to the object as shown...
Consider the vector field F(x, ) (4x3y -6ry3,2rdy - 9x2y +5y*) along the curve C given by r(t)(tsin(rt), 2t +cos(xl)), -2ss 0 To show that F is conservative we need to check a) b) We wish to find a potential for F. Let r,y be that potential, then Use the first component of F to find an expression for ф(x, y)-Po(x,y) + g(y), where ф(x,y) in the form: Differentiate ф(x,y) with respect to y and determine g(y) e Using the...
Prove that cos(3t)=4cos^3(t)-3cos(t). Use this to show that we can trisect any angle if we know how to solve a cubic equation c=4x^3-3x, where c is a constant. Then explain how to solve the equation c=4x^3-3x by intersecting two parabolas. Draw these parabolas.
(1) Let a (.. ,a-2, a-1,ao, a1, a2,...) be a sequence of real numbers so that f(n) an. (We may equivalently write a = (abez) Consider the homogeneous linear recurrence p(A)/(n) = (A2-A-1)/(n) = 0. (a) Show ak-2-ak-ak-1 for all k z. (b) When we let ao 0 and a 1 we arrive at our usual Fibonacci numbers, f However, given the result from (a) we many consider f-k where k0. Using the Principle of Strong Mathematical Induction slow j-,-(-1...
VI). Lct a). Show that b). Show that Fdr is not independent of path Hint: Compute fo, Fdr and fo, Fdr where C1 and C2 are the upper and lower halves of the circle r2y21.] c). Does this contradict the following Theorem Theorem. Let F- Pi +Qj be a vector ficld on an open simply-connccted region D. Supposc P and Q have continuous first-order derivatives and throughout D then F is conservative
VI). Lct a). Show that b). Show that...