Find the 45th term of the triangular numbers (1, 3, 6, ...) using the formula a b C d 946 990 1,035 1,081 'n = n(n+1) 2

Q: Determine if the series converges or diverges. Give a reason for your answer. ∞ Σ n=1 3 5 + Inn Does…

A:

Q: %A) .{ The solution of the separable differential equation- None of the Choices y = 2² + 2 Option 1…

A:

Q: Suppose xo = 2√3, yo = 3, Prove that 2xn-14-1 Xn-1+Yn-1 and Yn √xn Yn-1 for all n € N. (b)x=y and…

A: Hints: It is given that x0=23 and y0=3 and  xn=2xn-1yn-1xn-1+yn-1 and yn=xnyn-1 for all n∈ℕ.…

Q: Find the Fourier series expansion of the following periodic function: -2 <t<0 0<t <2 f(0-{_-3 =

A:

Q: 5x₁ + x₂x3 = 4 = 15 using: x₁ - 2x₂ + 5x3 = 12 a. Jacobi (use x₁ (0) = 0, x₂(0) = 0 and x3 = 0 and 4…

A:

Q: Consider the following problem; max f(x₁, x₂) = -x²-x² subject to (₁-1)³ ≥ x² Check whether the…

A: As per the question we are given an optimization problem with objective function : f(x1 , x2) = -x1²…

Q: Z -0.58 -1.63 $1.00.00.00 -1.800 Drag the surface to rotate it Indicate the number of each type of…

A:

Q: 25. Draw the following angles on a (separate) Cartesian plane and then create and complete a table…

A:

Q: Problem 3 Solve using method of Laplace: y" — 2y' – 3y = 0, y(0) = 1, y′(0) — 15

A: Given equation is y''-2y'-3y=0 Also given y0=1,  y'0=15   To Solve: using method of Laplace.

Q: Let yty + 0.1y³ and y(0) = 1.1. Use Euler's method to find approximate values of the solution of the…

A: Given: Euler's Method: For a given IVP y'=f(x,y), y(x0)=y0 the iteration is given by yn+1…

Q: Differential equation: t2y'' - ty' - 3y =0. What values of z is y(t)=tz a solution to the…

A:

Q: 39. Find an orthonormal basis 1, 2, 3 of R³ such that (G) span

A: Given,                        spanu1→=span123and        spanu1→, u2→=span123, 11-1

Q: For this activity consider that you are in the landscaping consultant business for a company…

A: Given: For this activity consider that you are in the landscaping consultant business for a company…

Q: y" + 4y = 1² + 8e', y(0) = 0, y'(0) = 7

A: we are given second order non homogeneous linear differential equation with constant coefficients to…

Q: (3) Suppose that x ≥ 2 and x = 2 + √√xn-1-2 for n € N. Use the Monotone Convergence Theorem to show…

A: Given: Here xn is a sequence specified by the expressions x0≥2 and xn=2+xn-1-2 for n∈N. Let's…

Q: Suppose xo = 2√3, yo = 3, Prove that Xn= 2xn-14-1 Xn-1+Yn-1 and Yn √n Yn-1 for all n € N. (b) x=y…

A: We claim that, xn&gt;yn&gt;0 We shall prove this by principle of Induction. We are given that…

Q: 3. It is given that sin(x) + cos(x) tan(y) = 1. Use implicit differentiation to find

A:

Q: Q3: Evaluate z + 1 $c (z6 + 5z5 + 4z¹) (z + 4) dz where C is the circle |z1| = 5

A:

Q: In the last year of the data, a car enthusiast spends $15,100 on a car of the given model that is in…

A: Given: Let us consider the given data, Enthusiast spends=$15100 Owner spends=$8300 Total…

Q: Determine the Fourier transform of the following: f(t) = {e/³t; -1<t<1 elsewhere 0,

A:

Q: 4. The roots of an auxiliary equation are r=2+3/, 1,-1. Write the corresponding homogeneous…

A:

Q: (a) Find the direction for which the directional derivative of the function f(x, y) = 9xy + 2y is a…

A: Formula for directional derivative Du→fP=∇f(P).u^=∇f(P)u^cosθ Du→fP to be maximum angle θmust be 0.…

Q: The following subset W of R² where W is the set of all vectors of the form CH with the usual…

A:

Q: Tomas and Emilio have a budget of $200 to plan their party at a movie theater. The party room at the…

A: We have the inequality 17f+2+45.99≤200 We need to solve this inequality. Consider:…

Q: Let A = (0, 0, #, a) and let # be a binary operation from A X A to A presented by the following…

A:

Q: sin has been transformed. It now has amplitude of 10.1, a period of 26, a phase shift of 0.5 units…

A:

Q: Exercise 5 Let X = (a, b, c, d, e) and let T = {X, 0, (a), (c,d), {a, c, d], [b, c, d, e}} is a…

A: Introduction: Topological space is the generalisation of metric space. It is very significant in…

Q: Comment on using the Newton method to compute the root of the function f(x) = x¹/3, i.e., if your…

A: The given function is f(x)=x1/3. We have to explain whether Newton's method works in finding the…

Q: Find the Fourier series expansion of the following periodic function: t, f(t) = {_3", -2<t<0 0<t <2

A:

Q: (6) Find the limit infimum and limit supremum of the following. Write a brief and concise…

A: We know that if ( xn ) be a bounded sequence of real numbers. Then the greatest subsequential limit…

Q: D1(-1)n (x+2)" n3n

A:

Q: Using the method of undetermined coefficients, The general solution of the differential equation y"…

A: Let us consider the differential equation y''+Ay'+By=Q(x) To solve the equation using undetermined…

Q: Find an equation for the surface obtained by rotating the line z = 7y about the z-axis.

A:

Q: 100-gal tank initially contains 25% dye solution. A 40% dye solution is allowed to enter at a rate…

A:

Q: Find the exact value of each trigonometric function. A full solution is required.. a) sin 225° b)…

A:

Q: Q.2 Use ODE methods to solve the PDE: U₁+U₂=5, U(0, y) = −5,U¸(0, y) = 3y

A: Introduction: When the variable in a differential equation consists of a dependent variable that…

Q: 6. Consider the set Zn under the operation of multiplication. (a) Build a Cayley table for n = 5 and…

A: We now construct the cayley table fot (Z5,.) And (Z6,.)

Q: Complete the chart and sketch a possible graph of the function labelling key points. f(x)=; :-4)²(x…

A:

Q: Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

A: We need to determine and classify the critical points of the function: f(x, y)=4x2y-2x-y2.

Q: Find a particular solution to the differential equation using the Method of Undetermined…

A:

Q: Find the exact sum of the following series 3 0 In (²) 2 3 5 010 ( 17 ) - 1/1/2 ln 2 3 2 (²) - ²/3 2…

A:

Q: 9. (a) Express 2 2¹-1² as partial fractions. (b) Hence, compute the exact value of the following…

A:

Q: Consider the following nonlinear constrained optimization problem: Minimize f(x₁,x₂) = (x₁ − 2)² +…

A: As per the question we are given an optimization problem along with a candidate solution x*  which…

Q: Find the sloution of the given DE dy y-x dx y + x = Yexact - y(0) = 1, h = 0.1 at x = 0.5 ? (find…

A: Introduction: Euler's method is a tool that is used to solve an initial value problem numerically.…

Q: 7. Consider the following table that displays the binary operation on the set (x, y, z). *…

A:

Q: Using the method of undetermined coefficients, a particular solution of the differential equation y"…

A:

Q: 8/14 Let 1 < p < 0. For t = [0, 1], let xi(t) = 1, -{ 1, if 0 ≤t≤ 1/2 -1, if 1/2 <t≤1 and for n =…

A:

Q: Q4. Determine the Fourier transform of f(x) = www for x<a 0 for x<a

A:

Q: A) B) dx₁ dt dx₂ dt dx₁ dt dx2 dt dx₁ dt dx₂ Wh = x₁ + 2x₂ + 2x₁.x2 = x₁ + x₂-X1X2 is stable or…

A: Given :           A) dx1dt=x1+2x2+2x1x2    dx2dt=-x1+x2-2x1x2           B) dx1dt=-x1+x2+x12…

Q: (3) Write the equation of the plane which is perpendicular to the vector ñ² = (2₁-1₁-2) and touches…

A: To find- Write the equation of the plane which is perpendicular to the vector n→ = 2, -1, -2 and…