re with a constant electric current, if there is heat exchange between surface and the surrounding medium. Answer : u = a*uxx - hu + q, where h and q are certain constants.

Q: what is the vertex cover And give examples

A: We have to define the Vertex cover  and example.

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim 0 sin 2 -16 2. lim 4 (V+5)-3

A: 1. Here limx→07xsin 2x is of 00 form, so by applying L. hospital rule, we get limx→07xsin 2x =…

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Q: Find: 2. fx³jo(x)dx

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Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. а 3 (6, 2, -2), ь 3 (о,…

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Q: 1. Which of the following is false? * O If x > 0, then 1/x > 0. If x > 1, then x^2 > x. If x < y,…

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Q: EXAMPLE 3-2 Determine whether the following operators are linear or nonlinear: (b) Âf (x) = x² f (x)…

A: The solution is given as

Q: Suppose a, > 0, bn > 1 and lim an = 0, lim bn = 1. n-00 n-00 Define An = {x : an < x < bn}. Find lim…

A: We have to find limn→∞supAn and limn→∞infAn

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A:

Q: Evaluate the Laplace transform of tcos2t. O a. 6s2+ 24s+ 26 s°[(s+3)? +4} O b. s?+25 (s? – 49)? O c.…

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Q: + y = x?e3x. dx2 dx d?y 2 dx2 2. Solve by method of variation of parameter dy = ex sin x. dx 3.…

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Q: d?y 2y+y = x2e3x dy 1. Solve by D operator method dx2 dx 2. Solve by method

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Q: Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an…

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Q: Suppose the function g is defined by g(x) = { e-1/x x > 0 0, x 0, g(k) (x) Pk(x) e-1/x, for some…

A: Sol

Q: WHAT IS THE FOURIER EXPANSION OF THE PERIODIC FUNCTION WHOSE DEFINITION IN ONE PERIOD IS : F(t)- for…

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Q: sin x – e-* = 0, [0,1]

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Q: Find the best approximation to z by vectors of the form c,v, + C2V2. 3 1 - 6 2 - 1 V2 = - 3 3 1 The…

A: Solution

Q: 50 107 36 A = 25 54 20 31 66 21

A: This is a problem from linear transformation.

Q: Find the values of w, x, y and z in fraction form using (a)Gauss Elimination, (b)Gauss-Jordan…

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Q: Complete the integral(s) that defines L{f(t)}. L{f(t)} = dt+ dt Find L{f(t)}. (Write your answer as…

A: We have to find the laplace transform.

Q: Find: 2. Sx³jo(x)dx

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Q: A Line 32 Long jons te nap founson a a frow any, far apart are fhe fains p the hearest km?b Wpat!…

A: This is a problem of counting, finite math.

Q: dx dx 3. Solve the Cauchy-Euler equation x 4. Evaluate L (sin t - cos t)². 2. dy + 4x dx + 2y = e*.…

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Q: What is the chromatic number of the given graph?

A: We have to find the Chromatic number of the given graph.

Q: Find the eigenvalues A1 < A2 < Ag and associated unit eigenvectors u1, ủ2, üz of the symmetric…

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Q: equations, use phase flow, initial conditions, ndicate x and y nullclines and equilibria. (if…

A: Sol

Q: sinxcost ; 00 = 0, u(pi/2,t) = 0 ) =0, ut(x,0) = 0 %3D 00 = u. - sin x cos t, : u(0, t) = 0, E u(x,…

A: Sol

Q: Use the graph G below to answer the questions. V1 v2 ei e2 V3 V7 ез eii e6

A: If two vertices are connected by an edge, then the vertices are adjacent Therefore the vertices that…

Q: in the parabola 16y = 160- x2. Find the maximum area of the triangle if side s B and C is parallel…

A: Sol

Q: Consider the function defined by f(x,y) = 4x² + y? (a) Find the domain and range of f.

A: Given function: fx,y=4x2+y2To find: Domain and range of f.

Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Given W is a subspace spanned by the u's where y=322-1, u1=1101, u2=-120-1 AND u3=-1011   To Write:…

Q: WHAT IS THE FOURIER EXPANSION OF THE PERIODIC FUNCTION WHOSE DEFINITION IN ONE PERIOD IS: F(t) = for…

A: We have , Ft = 0 , -π &lt; t &lt; 0t2  ,     0 &lt; t &lt; π We have Fourier series ,  Ft = a0 +…

Q: [-2 2 -31 d the eigenvalues and eigenvectors of matrix A = 2 1 -6 [-1 -2 tyned answers are…

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Q: 13 14 6 8 -1 13 2 5 16 11 9 Example 4.4. Using the partition method, find the inverse of A = 7 3 9.

A: We need to use partition method to find an inverse of matrix A.

Q: 5. Fill in the blank: For x, y E R. Equality in the Triangle inequality is satisfied, i.e. |x+y| =…

A: Let us consider x,y be any real number  then  Inequality Resultant xy&gt;0 x&gt;0 and y&gt;0…

Q: A Living a pom is 7:2m fog and 15 m wide. what ire gresesd wald 7 be of a joale plan qucun p a feale…

A: The given length of the room is 7.2 m. The given width of the room is 4.5 m. We need to find the…

Q: * The given matices , verify directly thart (RS)* -5*R* and (E) - p*i* 3 i . R= 3i %3D 1

A: The given matrices are: R=123i4, S=3i70, To prove: (RS)*=S*R*.

Q: All are equivalent but which among the following versions was due to Archimedes as recalled in his…

A: We have to identify which of the following was due to Archimedes.

Q: |e*y dx+e* dy; C: r(t) = (t+ 1, ),-1si<3 Exercise 97.

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Q: Let a (> 1) be an irrational number. Show that the kth convergent of the simple continued fraction…

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Q: aluating line integrals previously taught. What happens?

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Q: Bessel functions often arise in advanced engineering analyses such as the Modulation sidebands…

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Q: 2. Three different types of computers need varying amounts of four different types of integrated…

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Q: Let L be the linear transformation from R2 R? which is a reflection in the horizontal axis followed…

A: Sol

Q: A ball with mass 0,15kg is thrown upward with initial velocity 20 m/s from the roof of a building…

A: Find the maximum height above the ground the ball reaches. The right model is now…

Q: Find partial derivative, zg and Zy for the following function: e 2x²+3y Z =

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Q: (a) Let Re denote the rotation matrix cos e Re sin@ sin Cos 0 Show that the set of Rg. where 0…

A: (a) To prove:  The set {Rθ=cosθ-sinθsinθcosθ | θ∈ℝ} forms a group under matrix multiplication. (b)…

Q: C) lie in the parabola 16y = 160 – x². Find the maximum area of the triangle if side rtices B and C…

A: Sol

Q: Find the eigenvalues A1 < A2 and associated unit eigenvectors ü1, ủg of the symmetric matrix 7 61 A…

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Q: Describe the graph of the equation. r = 16 cos ti + 7 sin tj - k O It is an ellipse in the x = -1…

A: