g(x, y) = = sin(xy) xy Prove that g is continuous on R². if (x, y) = (0,0) if x = 0 or y = 0.

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Q: 1. Given that the third term of a geometrical progression (GP) is, and the fifth term is, find the…

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Q: (B): Find the general solution of O.D.E y" – y = sinh(x) + cosh(x)

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Q: Question 2: Evaluate 4, y = 0, z = 0, z = 1. III. xyz dV where S is the solid bounded by y = √, x =

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Q: 2. Use LU decomposition with partial pivoting to solve the following problem. 2x₁ +5x₂ + x3 = -7 2x₂…

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Q: Let an be recursively defined by a₁ = 3/4, an+1 = n 1. Find lim an. n-∞ n n+2 a² for

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A: given f(-x)=-f(x)⇒function is oddlimx→4-f(x)=∞ andlimx→4+f(x)=-∞⇒vertical aymptote at…

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Q: -1 5 7 For the given matrix 4 = 0 -3 0 -4 7 2 (a) Find all eigenvalues and present them in the…

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Q: 3. A man invests R2500.00 at a compound interest rate of 8% per annum. If at the end of the year, he…

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Q: Consider the following vector function. = (st, 1½-12², 12²) (a) Find the unit tangent and unit…

A: Given that the vector function is                                      r(t)=5t, 12t2, t2.

Q: Solve the system Solve the system -2x+y=-3 by elimination. 7x - 3y = 9 8 (4x+10y = -11 (y = 12 - 6x…

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Q: part b and c are not correct, please solve them

A: Given: A bacteria culture starts with 140 bacteria and grows at a rate proportional to its size and…

Q: Problem #5: Expand the following function in a Fourier series. f(x) = 5x² + 10x, 0 < x < 4 Using…

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Q: Solve the following ordinary differential equations: 2) (3y³-x) dx = 3xy-dy

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Q: You bought a collector’s oil painting for R20 000. The value of your oil painting appreciates at 20%…

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Q: Calculate the domain of the following function: a) h(x) = √x + 2 X+2 b)q(p) = 3p-40 c) P(x) = 100

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Q: For each of the following linear difference equations, please find an expression for yn, the…

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Q: Determine the graph of the cylinder z=6y2−1.  Choose the correct graph of the equation.

A: Answer:-Option (C) The equation z= 6y2-1 will have a 2D plot in z-y plane. Now its 3-D graph will be…

Q: If Zk e C;k = 1,2,3,…,n. Prove a)Ro(Στ.) (SROZ - ΣRezk k=1 k=1 Dim(Στ.) (gimz) k k=1 k=1

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Q: Problem 10: Let V be a finite dimensional vector space and T: V → V a linear map. Let W be a…

A: We will prove this statement by induction   on k.   Base case: k = 1. In this case, we have   only…

Q: Let y(t) be a solution of y'= y(1) such that y(0) = 12. Determine lim y(t) without finding y(t)…

A: Solution is given below:

Q: Inventory Microbucks Computer Company makes two computers, the Pomegranate II and the Pomegranate…

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Q: di. Classity and Solve 2 ў хах-ўdx= ухаўтуну ух т У+ жу=х 2X

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Q: Foreclosure Crisis Starting in 2010, on the heels of the 2007-2009 subprime mortgage crisis, the…

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Q: Suppose that news spreads through a city of fixed size of 200000 people at a time rate proportional…

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Q: Find the eigenvalues of the triangular or diagonal matrix. (Enter your answers as a comma-separated…

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Q: Use inverse matrix method to solve the simultaneous equations: x+y+z-4 = 0. 2x-3y + 4z-33=0…

A: Given ,  x + y + z = 4 2x -3y + 4z = 33 3x -2y -2z = 2

Q: Let H(x)= " plays hockey". Let B(x) = "x plays basketball". Which statement below means "If everyone…

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Q: Let D be the conical solid shown with the boundary of D consisting of the surfaces L and C where L…

A: Eliminate R and θ0 appearing in the expressions so that the relation (to be derived) between the…

Q: se matrix inversion to solve the given system of linear equations. (You previously solved this…

A: we will use this for matrix inversion Ax=Bpremultiply by A-1on both sidesA-1Ax=A-1BIx=A-1Bx=A-1B…

Q: a survey of 1000 adults aged 18 and older, the following question was posed: "Are other travelers'…

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Q: Using the method of bisection, and starting by observing that √11 lies between 3 and 4, give a…

A: Given 11 lies between 3 and 4. Given the maximum error is 0.1.   Bisection method is used to find…

Q: 5. The region R is bounded by the curves x = y² + 2, y = x - 4, and y = 0 (see figure). Jove R y=x-4…

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Q: In this problem we show that the function f(x, y) = 21-y lim (1,2x) (0,0) I+y 2x - Y x + y does not…

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Q: Determine whether the function is a linear transformation. T: M2,2 → R, T(A) = a + b-c-d, where A =…

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Q: Find the work done by an ideal Carnot Engine by calculating the area defined by the region R within…

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Q: Obtain by means of riemann sums the area under the curve of f(x) x² +11x - 26 from x=3 to x=7

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Q: A "S number" is a positive even number that is not the product of two even numbers. A "B number" is…

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Q: Express the characteristics of the following sets of points, in terms of: closed or open, connected…

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Q: solve the given initial-value problem. Q. y′−2y =u2(t)et−2, y(0)=2.

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Q: Use differentials to estimate the volume of metal in a closed tin can with diameter 8cm and height…

A: Given that : the diameter of the closed tin can (d) = 8 cm          ⇒  Radius  (r) = d/2 = 4 cm…