1. Prove that if f(x) is bounded and measurable on E, and c is any constant, OMNIA then S, [f(x) + c] = S, f(x)dx + cm(E). %3D

Q: 3. Graph the polar equation and find the area of the region. Interior ofr= 6+3 sin 0

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Q: Find a linear transformation L: R4 → R³ whose kernel is spanned by the set S = 2

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Q: Exercises 1. If X1, X2,..,Xn constitute a random sample from a population with the mean u, what…

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Q: n* In n ,4 b) Is the series is absolutely n8 – 2 n=1 convergent or divergent? justify your answers.

A: Test for converges of the series, using limit comparison test

Q: Find the potential function f for the field F. F = (y - z) i + (x + 2y - z) j - (x + y) k   a)…

A: Let us find the potential function

Q: 2. If the product of matrices cos² 0 cos e sin 0 A = cos 0 sin 0 sin 0 cos² cos o sin sin? cos ó B =…

A: Solution :-

Q: Q/ Use Lagrangian polynomial to find f'(2.1) from the following table 1 2 3 f(x)| 10 17 22

A: Numbers of data point set is 3, so the degree of polynomial will be at most degree 2.

Q: 6. 'The mapping T :R³ → R? is defined as T (x, y, z) = (x + 2y+ 3z, x + 3y + 2z) is a linear…

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Q: Consider that, we have the following initial value problem: y' =-+). 1sis2 y(1) = -1 : Use Taylor…

A: Using Taylors series upto second order

Q: doorway Vertex A B C D E

A: The Euler path exists and it is C→F→E→F→A→F→D→F→B→A→D→E

Q: Answer the following using Jacobi Method. Show complete solutions. The answer should have atleast 5…

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Q: , How many ways are there to distribute r+s identical balls among five different children such that…

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Q: 2) Consider the fiunction g defined by (TX/y)+ glx, y) = COS log3 (x-y) la) determine dydx

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Q: Find the work done by F over the curve in the direction of increasing t. F = -7y i + 7x j + 9z 7 k;…

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Q: For X and Y normed linear spaces, let {Tn} be a sequence in L(X,Y) such that Tn → T in L(X,Y) and…

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Q: FIND THE LENGTH OF THE CURVE 9y = x(x – 3)´ from X = 1 to x = 4 %3D 10

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Q: dz IV. Suppose z is a function of x and y, and a? – y? = 2"e©y. Solve for %3D dx

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Q: (2) Solve the Laplace equation with the following boundary condi- tions. Uzr + Uyy = 0, 0 < « < a,0…

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Q: Q3 By using the derivatives transformation find the transfer of the function a" (t) + æ(t) =…

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Q: find Numaerical Inteqration by 3-pointsta 3. Sinx (2V3 +3 Idx

A: The given problem is to the approximate of the definite integral using Numerical integration of 3…

Q: |Suppose that dy = y3 + y? – 9y – 9 dx %3D and that the point (13, –2) lies on the graph of (x, y).…

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Q: 1. Raul has a wall 4 units long and 2 units wide in the Cartesian plane centered on the origin. On…

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Q: Let T be a linear transformation from V into W. Then T is non – singular if and only if T carries…

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Q: Given: surface G : 9x^2 - 4z^2 = 9y (a) Give the equation of the trace of G on each coordinate plane…

A: Solution :-

Q: а. 10х, + 2х, — х, 3D 27 — 3х1 — 5х, + 2х; — —61.5 X1 + x2 + 6хз — — 21.5

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Q: 2. The Lorenz curve of a particular society is given by L(x) = Ax? + Bx. %3D Suppose that the…

A: We will use given values in Lorenz curve and Gini index to create equations for A and B , Then solve…

Q: Show that the function f defined by 1, (x, y) = (1, – 1) f (x, y) = x² + y (x, y) # (1, –1) x + y is…

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Q: 4.) Consider the function g defined by g(x, y) = car ( 7X Jj ) + logg(x-y) does 9 have the maximum…

A: Given: gx,y=cosπxy+1log3x-y

Q: Consider the function defned by f(X, y) = y-ex (a) Find the domain and ran ge of f. (b) Draw a conto…

A: The graph of a three dimensional surface is represented by the equation: z=f(x,y). The graph of a…

Q: 2 1. Consider the quadric surface S;: + (y + 1)² – e-3)° = 1 3 (a) Find an equation for the trace of…

A: The solution is given below

Q: ITEM 3. Prove: If A C B and BC C, then ACC.

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Q: 9. Consider the column vectors u and v in R" cos(0) cos(20) sin(0) sin(20) u = v = cos(n@) \…

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Q: 4. JK Is tangent to the circle. Solve for x. 5. Both segments are tangent to the circle. Solve for…

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Q: Calculate the instantaneous rate of change of g at the point (4, 1, 2) in the direction of the vec…

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Q: Test the convergence and divergence of the following: nin! 1. En-0 2. En=1 (2n)! 3. Ln=1 cOsnn n%3D1…

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Q: . A rectangular tent is made to have a square base with two partitions inside that divide the tent…

A: We will find the function to be minimized and then use calculus to minimize it

Q: oposition 4.21 The path components of X form a partition of X. O Each path component is contatined…

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Q: 4) Using Rational Root Theorem and Descartes' Rule of signs. Find all roots of f(x)= x° + 8. What…

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Q: 2422+1 FindtheRes

A: In this question, the concept of the Residue Theorem is applied. Residue Theorem ∫cfzdz=2πi∑residues…

Q: * dy/dx=(x+siny)/(2y-xcosy) is an exact equation false O true O

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Q: A store owner bought 28 swimming caps for P 2, 436.00. He sold 3/14 of them at P 100.00 each and…

A: Given , Cost price of 28 swimming caps = P 2436 Now, (3/14) of caps = 28 x (3/14)= 2x3 = 6 Selling…

Q: A rectangular tent is made to have a square base with two partitions inside that divide the tent…

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Q: Find the volume of the solid whose base is in the first quadrant bounded by y = 7- 7x, the x-axis,…

A: To find the volume of the solid whose base is in the first quadrant bounded by the below curves, and…

Q: 5. A rectangular tent is made to have a square base with two partitions inside that divide the tent…

A: The total surface area of an object refers to the two-dimensional space the object's surfaces…

Q: log (a cos 6+b sin 6) do=w log 1, a>0, b>0 %3D

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Q: 25. (i) Calculate the determinant of thenxn matrix (1 1 1 ... 1 1\ 1 0 1 ... 1 1 1 1 0 1 1 ... A = 1…

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Q: k Ink is Ln=1 (k+1)3 In k а. k2 In k+ln 1 b. k3 In k+ln 1 с. k2 In k d. k3

A: Serie and sequence, limit comparison test

Q: USe the Euler method's Selvetue:- yく): ピhwe.2 ノ

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Q: VII. Use Lagrange Multipliers to solve the following: Maximize f(r, y, z) = 4.x + 2y +z subject to a…

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Q: Let U be a universal set and A, B, C CU. ITEM 1. Prove: A n BCAUB

A: # as per the guidelines we are entitled to solve one question at a time please resubmit the other…