Q1- Find all the second-order partial derivatives of the function: -1 s(x, y) = tan¯¹(x)

Q: Determine the directional derivative of X²Yz +4XZ² at the point P(1,-2,1) in direction a=2û - j +² R…

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Q: (a) Define a metric space (X, p). (b) Let p: R+ → R+ be a function defined by ln (2). Prove that p…

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Q: Find the radius of convergence as n goes to infinity of (log n)2 xn.

A: The given series is                                     ∑n=0∞log n2xn

Q: ¹t-In(t² + 1) te [-3

A: Given that C be x=t(t2+1)-12y=2t-2tan-1t-lnt2+1, t∈[-3,3] therefore, dxdt=1t2+1-122t2(t2+1)-32…

Q: Which one is a correct symbolization of the following sentence in FOL? "Only happy poets like all…

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Q: π containing both lines and m. o both and a normal vector of . Using do ㅠ. adicular to any normal…

A: The symmetric equation of l is x+15=y72=z-312 From the symmetric equation of l, we see that a…

Q: F(s) = S-1 (s+3)(s²+2s+2)

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Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: Solution :-

Q: IV. Write the equation of the ellipse. 1) vertices at (-10, 4) and (2, 4); minor axis with length 10…

A: For an ellipse: It is known that: e=ca and b2=a2-c2. If the major axis is parallel to the x axis,…

Q: Which of the following is the homogeneous A. (3x - 5)dx = (4y - 1)dy B. xydx (x³ + y³)dy = 0…

A: A function f(x,y) is said to be homogeneous of degree n if for any scalar k ,  f(kx,ky)=knf(x,y). A…

Q: Let f(u, v) = (u - v, 1,u + v) and g(x, y, z) = xyz. Find the entry a12(i.e. the entry in the first…

A: As per our guidelines we are answer submit of only first three sub parts question of multiple sub…

Q: Find the elementary matrix E such that EC = A where 2 1 5 2 1 A = 3 0 -1 and C- 3 Communest 0 6 -8 2…

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Q: 1. Given the following matrices: 1 2 3 4] [4 2 468 A = B = 1 3 5 7 -1 2 2 4] a. [(AC)BT] - DT b.…

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Q: Q2: For the following LP model, find values of the first iteration tableau variables using simplex…

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Q: A n x n Hermitian matrix contains exactly k real entries. Show that k + n must be even.

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Q: An airplane is travelling at 620 km/h on a heading of 305°. The wind of 80 km/h is flowing from a…

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Q: What is the unit vector with the same direction as the vector v = 2i - 7j? Write as a linear…

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Q: The value of the following = (2+ sin 2x3) Using the trapezoid integration dx method, knowing that n…

A: Sol

Q: 41. Two straight roads diverge from an intersection at an angle of 60°. Two cars leave the…

A: Cosine formula  In a triangle ABC if a.b.c denotes sides opposite to angles A,B,C respectively i.e.…

Q: Show complete work Prove the orthogonality of eigenvectors, and demonstrate it with a 2 DOF system…

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Q: Consider the solid formed by the points outside the hyperboloid x² + y²-z² = 8 and inside the…

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Q: 2. Using laplace transforms solve for x and y: dx dy + dt dt 2dx dy + + x +y = 3 dt dt subject to…

A: The solution is given as

Q: Dest Sourcest L 2 3 4 Demand 1 5 15 3 7 2 10 2 5 کا 3 15 O 4 2 O Supply 20 Lo 15 15 using Vogel's…

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Q: Show that the vector-valued function shown below describes the motion of a particle moving in a…

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Q: Homework 3 Draw the following Polar Curves:- 5. r² a² sin20

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Q: 17. (15pts) Let relation G be a subset of the cross product of the natural numbers with the natural…

A: Using the definition of Reflexive relation,symmetry relation, Transitive relation, Antisymmetry…

Q: Consider the function defined by f(x) = e-x² . a. Using the Maclaurin series expansion of e*, to…

A: Given function is f(x)=e-x^2

Q: Find the arc length parameter along the curve from the point where t=0 by evaluating the integral s…

A: Solution

Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky + k² = 0 and…

A: Using cylindrical shell method

Q: Prove that the function f(x)=Lnx, defined on the domain is a concave function. For this purpose,…

A: Follow the steps.

Q: Sheet modeled on 3D Cartesian space defined as Z = 4x² bounded over region (X,Y) = [0, 1] × [0, 2].…

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Q: ΑΣ (Inn) Σ 4 n n=2

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Q: ((bv d)-v(bad)) → (b → d)- Aldis S

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Q: A food store surveyed 50 of its shoppers as to whether they had purchased bacon or steak during the…

A: Note: Hi! Thank you for the question, As per the honour code, we are allowed to answer three…

Q: : Prove that the function f(x)=Ln x, defined on the domain R₁, is a concave function. For this…

A: Here Hessian matrix going to be 1×1 matrix.

Q: Consider the market for lollies where if the price per lolly is $4, total market demand for lollies…

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Q: Find the flux of the vector field F = [x,y,z] through the oriented surface S: z= x^2 + y^2, z <= 1…

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Q: EXERCISE 2.1 Derive the expression of the normal vector K(t) of the parametric curve P(t) = (−1,…

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Q: For item 17-18. Let R be the partial ordering on A = {1, 2, 3, 4, 8, 12} defined by xRy if and only…

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Q: Q3- Sketch the region of integration and evaluate the integral: In8 Iny ex+y dxdy

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Q: Find the flux of the vector field F = [x,y,z] through the oriented surface S: z= x^2 + y^2, z <= 1…

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Q: Solve step by step in digital format 2x - 6 b) lím X-00 x²-9

A: Solution

Q: Example: Test the following series converges. a. { In ( n + 12 ) n+2 M=1 or not

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Q: Q2- By using Chain Rule, find au/ax, du/dy, du/əz at (x, y, z) = (√√3, 2, 1) P-q u= p=x+y+z q=x-y+z,…

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Q: Consider the sequences 2, 5, 12, 29, 70, 169, 408, ... (with ao = :2). (a) Describe the rate of…

A: consider the sequence 2,5,12,29,70,169,408...... (a) describe the rate of growth of this sequence.…

Q: (a) Describe the symmetries of the Figure below. Assume that o is the centre of rectangle abcd. (b)…

A: (a.) To describe: The symmetries of the given figure, assuming that o is the center of rectangle…

Q: Calculate the vector field flux leaving F(x, y, z) = xi + yj + zi solid bounded by the surfaces x² +…

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Q: pls

A: We solve by LU factorization.

Q: GIVEN: f(x) = 2x³ − 2x¹ +10x² -2=0 Using NEWTON'S METHOD, determine new estimate after 2nd…

A: We have to determine the new estimate after second iteration by Newton’s Method. Newton's  Method…

Q: Find the equation of the straight line parallel to the line 2x + 3y = −4; containing the point (−5,…

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