INSTRUCTION: Prove or disprove 1. Show that f: R-{-}→ R-{} defined by f(x) 3x-5 = is bijective. 2x+1

Q: 2. Let G = {(a, b)|a, b € R, a ‡ 0}. Define a binary operation * on G by (a, b) * (c,d) = (ac, b+d)…

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Q: 5. In each of the equation below, find an equation in rectangular coordinates. a)p+ 3 = e b)r -2 = 3…

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Q: 5. Consider the function f: Z15 → Z15 given by f([n]) = [n³]. Show that f is a function, and…

A: Given is a function f:ℤ15→ℤ15 by f([n])=[n3]   To Show: f is a function.   To Determine: Image of…

Q: Consider A= (0, 4, 2), B =, (6,-1,0) and C = (3, 0, 1). 1 (a) Find the unit vector having the same…

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Q: Example 7.4. Using Newton's backward difference formula, construct an interpolating polynomial of…

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Q: slope of IJ = slope of JK= slope of KL =

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Q: (d) A curve is defined by the parametric equations: -21 x(t)= e' cos 2t, y(t) = e²¹ sin 2t dy…

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Q: Show that for A and B of n×n order with complex enteries the matric Ab need not be similar to BA ,…

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Q: Evaluate // (1+x² + y2) dV, where E is the region bounded E by the surfaces z = 6y2 - 9x², and z = 6…

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Q: At a point where y' = 0, if y changes from positive to negative as x increases, Ay is maximum By is…

A: We want to find true option.

Q: Question 12 The temperature T at a point (x,y,z) of a solid is given by the function T(x,y,z) = 2x²…

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Q: Suppose m, n ∈ Z + are relatively prime. The function f : Zmn → Zm × Zn defined by  f([Z]mn) =…

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Q: Find the center of mass for the region bounded by y=3-e&x= 2 in the first quadrant. a.…

A: Centre of mass of bounded by the curves in first quardent

Q: Solve f(x) Sin e* (4 nodes) Using Gaussian Integration (Numerical Methods) [ f(x) dx

A: Given function is f(x)=sinex We have to calculate ∫-11sin(ex)dx Formula for 4-point gauss quadrature…

Q: A ={ 1, 2, 3, 4, 5, 7)} B = { 1, 5, 6, 8} 22. Concatenation of string {(x,x) & A} 23. Concatenation…

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Q: Find an approximation of the area of the region R under the graph of f by computing the Riemann sum…

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Q: After differentiating the last expression we obtain that 1 C(y) = sin 3y. Hence, we get 1 1 sin…

A: Given that, Cy=13sin3y                   1 and after differentiating the last expression, we get…

Q: Find the area inside r = 3 sin 30 and inside the circler = 3 sin 0 Note! (Draw the graph. Show the…

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Q: A breeder reactor converts relatively stable uranium-238 into the isotope plutonium-239. After 15…

A: Given: A breeder reactor converts the relatively stable uranium 238 into isotope plutonium 239.

Q: Problem 3 Using Variable Separable, solve x² (y + 1) dx + y² (x - 1) dy = 0

A: Given differential equation is x2(y+1)dx + y2(x-1)dy = 0

Q: x + 2y ≤ 40 2x + y ≤ 40 Use the following constraints to maximize z = 3x + 2y. { x + y ≥ 10 x>0 y 0…

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Q: 2. Solve, 6 0 1-0 10 OC

A: To find the matrix multiplication :-

Q: Let C₁ be a straight line in the Argand plane from (0, 0) to (3, 3), and let C₂ be the path…

A: We have to calculate the following integrals i∫C1z2dz  and ii∫C2z2dz where C1 and C2 are given…

Q: U A B C

A: We want to find true option.

Q: Find power series solutions for the following. Write at least first THREE terms for each seri 2.…

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Q: 1. For the matrix A=12²5¹ 7 3 6-12-5, (a) Compute the characteristic polynomial f(x) = det(xI - A).…

A: We have to find the characteristic polynomial.

Q: In order to solve with y(0) = 1 we first (2y-5)dy = (3x² - e²)dr. After y²-5y = 2³-e²+c of…

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Q: 2. Prove the following, using induction: (a) If an+1 = an/(an+1) prove that an = ao/(nao +1) for all…

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Q: he outward flux is Type an integer or a simplified fraction.) he counterclockwise circulation is.…

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Q: ? 4. Show that the sequence {fn}, where nx fn(x) = XER 1+n²x²⁹ is point-wise convergent but is not…

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Q: Use the second Taylor polynomial P₂ (x) for f(x) = x² + cos(x) about xo = x² + cos(x) about x = 0…

A: Given function is fx=x2+cosx. We have to evaluate ∫01fxdx by using the second Taylor polynomial P2x…

Q: 22 Find the PALU factorizations (and check them) for 0 1 1 A = 1 0 1 and A = 2 3 4 1 2 0 24 1 1 1 1

A: Solution :- As per guidelines I submitted only first question. If you want all question the repost .…

Q: The trace of a square n × n matrix A = (ażj) is the sum a11 + ª22 + + ann of the entries on its main…

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Q: Match each of the following with the correct statement. A. The series is absolutely convergent. C.…

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Q: Let J = √x² + y2 + z² dV, Where E is the region given by : E x² + y² + z² ≤2 Expressed in Spherical…

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Q: Determine if the following series converges. If the series converges, determine if it converges…

A: The given series is ∑k=1∞k!kk+1 To find: the above series is converges or not.

Q: Find the ONLY particular solution of the given linear system: x+3y+z+2t=1 2x+6y+4z+8t=3 2z+4t=1. 1/2…

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Q: find the equation of the inverse of one-to-one function  n(y) - y^2+9, y≥ 0

A: We know that x = y2 + 9 is a parabola with the vertex at (9, 0). The graph that is shown below…

Q: A firm faces the production function Q = 4K0.5L0.5 where K is capital and L is labor. a. Find the…

A: Note: As per our guidelines we are supposed to answer to only 3 sub-parts Q=4K0.5L0.5 where K is…

Q: Rest I Source 1 2 3 15 12 3 Demene 20 2 3 2 8 7 2 4 Supply 25 15 12 52 3 25 7 using North west…

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Q: 3. Consider the function f: IR→ (0,1] defined as f(x) = x² +1 (a) Prove that f is not one-to-one.…

A: Given function is f: ℝ → (0, 1] such that f(x) = 1x2+1

Q: solve the following system of equations: x'=dx/dt=7y+7e4t y'=dy/dt=5y-3e-5t

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Q: 4. Find the area of portion of the sphere x²+y²+z = 9 between the planes z = 1 and 2 = 0. Draw the…

A: Surface area of a surface z=f(x,y)  A=∫∫D1+fx2+fy2dA Here D is a point on xy plane

Q: Let A be a non-empty set of positive numbers, which is B={re R:1/xe A}. Prove that B is bounded…

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Q: Use the variation of parameters formula to find a general solution of the system x'(t):

A: Given,        A=17137, f(t)=5-5

Q: 3 2 1 Let u [-]--[-]-[] -3 V 2 and w= 1 0 -1 4 (a) Show that B = {u, v, w} is an orthogonal basis.

A: The given vectors are:  u=3-30, v=22-1, w=114. (a) To show: {u,v,w} is an orthogonal basis. (b) To…

Q: Use a parameterization to find the flux The flux is SSF n da of F = 2²1+xj-32k in the outward…

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Q: Question Suppose that you are estimating sin (0.6) using the second Maclaurin polynomial for sin…

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Q: Find the general solution of each of the following partial differential equations 9uxx-21Uxy + 49Uyy…

A: Find the general solution of each of  partial differential equations  9uxx - 21uxy + 49uyy = 0

Q: Problem 1: Obtain ODE by eliminating arbitrary constant A, B, and C y = A e²x + Be* + C

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