Let f: R+N+ with f(x) = [x²]; that is, f(x) returns the square of x rounded up. Characterize f in terms of whether it is injective, surjective and/or bijective. This is not a formal proof, but briefly explain you reasoning.

Q: (a) Let f(x, y) = x² + y². Plot the vector field Vf and the level curves of f on the same plot. (b)…

A: A function fx , y=x2+y2. To Find: a) Plot the vector field and the level curve of f. b) Do your…

Q: (b) Let g be the element 1 2 8 5 1 2 3 4 5 6 6 4 7 8 9 10 11 11 9 7 10 3 of S11, written in two-line…

A:

Q: Antonio found some games that he wanted. The regular price was $161. On black Friday they were on…

A: Antonio buy games on Black Friday or Cyber Monday? The procedure is given below

Q: 8. Show that {u,,,,} is an orthogonal basis for R³. Then express x as a linear combination of the…

A:

Q: e. Prove the following for all n ≥ 1 using weak induction : n (a + b)² = Σ(n)a(n-¹ f² (n—r) fr…

A: Using weak induction we solve this problem.

Q: Q4. Solve numerically by using the improved Euler's method dy-√√xy + 1 dx = 0 with y(0) = 1 for…

A:

Q: In this problem you will solve the differential equation (x + 2)y" - (11-x)y' + y = 0. (1) By…

A: Using frobenius method to solve the differential equation

Q: Azad sold some books at $12 each and used the money to buy some concert tickets at $60 each. He had…

A:

Q: . (a) Let R be a ring. Prove that (ab) = (-a) b for any elements a, b = R. - (b) Let R be a ring,…

A:

Q: Evaluate 1² cos(x/2) x² -dx as an infinite series and find [ - cos(x/2) x² -dx.

A:

Q: Find the slope using the line perpendicular to y=2x

A: Given that, find the slope using the line perpendicular to y = 2x.

Q: Silvio is taking a Biology course and his average before the final is 88.2. The final is worth 30%…

A: Silvio is taking a Biology course and his average before the final is 88.2. The final is worth 30%…

Q: 2. The Hill family took out a loan to have a swimming pool built in their backyard. The fifteen…

A:

Q: Find the critical point set for the given system. dx | dt dy dt = 9-y² = 3x + 2y ... Select the…

A: The given system of differential equations is, dxdt=9-y2, dydt=3x+2y. To Find: Critical points. To…

Q: use Laplace transform to solve IVP a) y'-3y = 4, y(0) = 0

A:

Q: Find the domain of the vector-valued function t R(t) = tan-¹t² + —_— 3 + sin t² k. 1-1²

A: Given the vector valued function R(t)=tan-1t i^+t1-t2j^+sin t2k^. We have to find the domain of…

Q: Find the value of e x using series expansion e x = 1 + x + x 2 2! + x 3 3! + · · · for x = 0.5 with…

A: Given that: ex=1+x+x22!+x33!+... We have to find n for which : e0.5-Pn0.5=Rn+10.5<0.005 Now,…

Q: Find the day of the week you were born, and of your birthday this year.

A: We assume that on the date 01.01.01 the day was monday.  Now, from start of the years (01.01.01), We…

Q: Odic function. Compute the Fourier series of f: Pn sin(nt) = cos(nt) + sin(nt).

A:

Q: Determine where the following function is differentiable? Where is it holomorphic? Determine the…

A:

Q: 28. Using the method of reduction of order, show that if 7₁ is a repeated root of r(r-1) +ar+ 3 = 0,…

A:

Q: Express the decimal expansion 0.1524 as a fraction in lowest terms

A: A decimal expansion 0.1524. To Find: Express the decimal expansion 0.1524 as a fraction in lower…

Q: Use spherical coordinates to evaluate and the sphere x² + y² + z² = 4. [] [² z dV, where E is the…

A:

Q: Use a computer algebra system to find the mass and center of mass of the lamina bounded by the…

A: Given that r= 4 cos 3θ (-π/6) ≤ θ ≤ (π/6) ρ=k we have to find mass and center of the lamina

Q: Solve the system graphically, and indicate whether each solution region is bounded or unbounded.…

A: The given system of inequalities, x+4y≤413x+y≤354x+5y≥65 We have to graph the solution region.

Q: Graph the curve whose parametric equations are given and show its orientation. Find the rectangular…

A: Given x=8cost and y= 9sint where 0≤t≤2π   t x y 0 8 0 π/2 0 9 π -8 0 3π/2 0 -9 2π 8 0

Q: 11. The position of an object subject to uniform circular motion around the origin is given by (see…

A:

Q: Use the vectors in the figure at the right to graph the following vector. 3v+u-2w Select the figure…

A: The graph of the vectors u, v, w are given, we have to sketch the equivalent graph of the vector…

Q: Let S represent the amount of steel produced (in tons). Steel production is related to the amount of…

A: Min: 50L+120C S.t    15L0.2C0.8=55000L,C ≥ 0

Q: Find general solutions of the linear systems. If initial conditions are given, find the particular…

A: Here the equations are given by x'' = -4x + sin t, y'' = 4x - 8y. The general solution of the linear…

Q: 4. Find the equation of the plane through the given points. (a) (1,1,2), (0, 0, 1), and (-2, -3,0).…

A: We have to find equation of plane passing through given points in part a) and part b) Concept…

Q: In the study of statistics, a joint density function z=f(x,y) defined on a region in the x,y-plane…

A: A function that describes the probability distribution of two or more random variables is called a…

Q: The table below shows the estimated world population in the given years, rounded to the nearest…

A: Year 1900 1950 1999 2011 Population (in billion) 1.7 2.5 6 7

Q: Construct a graph with vertices F, G, H, I, J, K, L that has an Euler circuit and the degree of F is…

A: The given vertices are, F, G, H, I, J, K, and L. The degree of F is 4. An Euler circuit is a circuit…

Q: The matrix A₁ = -4; 7₁ A = has the following eigenvalues and eigenvectors = -6 (₂₂) 2 2 3 (-1); A₂ =…

A:

Q: Find the linearization z' = Az of the system I'= y = at its equilibrium point (x, y) = (0,2). [84] 1…

A:

Q: Q3. Solve the following system of linear equations by a direct method: 3x + y - 4z = -1 4x - 3y + 5z…

A:

Q: Consider the graph of a function f(x) below. Calculate (in any way you wish) an estimate for the…

A: Suggest you to read part (b) first before going to part (a).

Q: 13 3] Let A== -10 Find two different diagonal matrices D and the corresponding matrix S such that A…

A:

Q: The first motorist paid $49.80 for 12 gallons of gas and 2 quarts of oil. The second motorist paid…

A: The first motorist paid $49.80 for 12 gallons of gas and 2 quarts of oil.The second motorist paid…

Q: The trendline is Y=0.918x+1.7355 and R^2 is 0.8237 If a student plugs the value 80 in the trendline…

A: According  to question,  The value 80 represents a certain input or independent variable that was…

Q: e the method of undetermined coefficients to solve the given nonhomogeneous system. *-(:)** (*:)*…

A:

Q: -93 225 90 -30 72 30 Find an invertible matrix P -20 50 17 and a diagonal matrix D such that D =…

A: The matrix is: A=-9322590-307230-205017. We have to find an invertible matrix P and a diagonal…

Q: You bought 0.875 kilograms of mixed nuts. What was the total cost, in dollars of the mixed nuts that…

A:

Q: Any sets A, B, C, formally prove the statement (A n B)-C=(A-C) n (B-C) 1) Element argument method…

A: Sets -A, B, and C

Q: nis fixed, show that both 3-terms Newton forward interpolation formula and Lagrange interpolation…

A: We have been given a table of data, x x1 x2 x3 x4 x5 f f1 f2 f3 f4 f5 x lies between x1 and…

Q: If a sports forecaster states that the odds of a certain boxer winning a match are 5 to 3, what is…

A: We have to find probability that boxer will win the match using given data. Formula required: 1)odds…

Q: 4) A mysterious card-playing squirrel offers you the opportunity to join in his game. The rules are:…

A: To calculate the expected value, we need to multiply the probability of winning by the amount won…

Q: Consider the graph given above. Add an edge so the resulting graph has an Euler path (without…

A: Euler path is the path should cover all the edges of the graph exactly once. No edge cover for two…

Q: Nine more than half the number n is no more than -8 . Find n.

A: