Q5: Fill in the blank:

Q: Given the following set of the vectors from M22 11 0 0 1 0 0 1 S = 0 0 1 1 0 1 11 Sis the spanning…

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Q: fined the genral solution

A: Given,        Dx2+Dy2u=0

Q: 9. Solve the given (matrix) linear system: [1 0 X' = 1 5 L2 4 -3] 1 X %3D

A: Solution :-

Q: nral solution D + D,)'u = 0 %3D

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Q: Prove that l17 is the only prime number of the form n²- 64.

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Q: Consider the vector v = (5 1 -3) in R3. v belongs to Span{(2 -1 0), (1 2 -3)}. %D Select one: True O…

A: Spanning set

Q: '2x2 + 1, x 1 For parts a-c, compute the limits algebraically. Show all work clearly, using proper…

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Q: o f > 0 and f" 0, for a > 3.

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Q: 1 2. Given the matrix A = -2 (a) Use the power series definition of the matrix exponential to…

A: Given a 2×2 matrix A = 100-2 . We have to solve two sub-parts :                    (a) Use the power…

Q: Let f : R → (0, +∞) be differentiable. Suppose that f' has no zero. If lim→0 f(x) = %3D 0, then…

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Q: Second question: logarithmic functions Draw and explain y = 150(0.073) in the form y = aekt

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Q: Find the volume of the solid under the plane z = 3x + y and above the region determ

A: Given the plane                       z=3x+y and                y=x7,  and   y=x

Q: a) Given the vectors in R3 v, =(11 -3), vz= (1 -3 1), v3=(-3 11) Using the system of linear…

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Q: -1,0 -5 1,0 -3 Let f(x) = S2 for 0 <a <2, for 2 <x< 4. Compute the Fourier sine coefficients for…

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Q: 1. Let X={a,b,c} and Y={1,2} then X×Y ={(a,1),(a,2).(b,1).(b,2),(c,1).(c,2)} - Consider U =…

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Q: We want to find the dimensions of the rectangle with the largest area that can be inscribed in the…

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Q: 1 -5e iwt dt + -jwt | 5e -jwt dt -1

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Q: Suppose we ALREADY KNOW that this field is conservative in Octant I: F (x, y, ±) = In (æ) + =, In…

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Q: Find the centroid of the region bounded by y = x^2, y = 0, and x = 1.

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Q: Critic points of an equation problem: Consider the equation f(x, y) = -x* - y3 – 4xy – 6x – y In the…

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Q: 5 x? + y? = 16, y² - x = 4.

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Q: 3. Verify the divergence theorem for A = 2xy i – yj + 4xz k taken over the region in the first…

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Q: Find the solution of the equation = e cos y dy? which tends to zero as x → 0o and has the value cos…

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Q: dy+ydk=Xcasx-dx-

A: Solution:-

Q: Find all integral solutions of the linear Diophantine equations 6x + 11y = 41. Use attached photo…

A: Using division algorithm. Integral solution it may be positive, negetive or zero .

Q: 3.) The time t in seconds that it takes for a pendulum to complete one full swing is given by the…

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Q: 9. Consider the R region shown in the following figure, which involves the curves of equations: 22 +…

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Q: Let V = R be the set of positive real numbers. We define addition and multiplication with standard…

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Q: a) Consider the set S= (+1, t+t, t+1}). Detrmine whether p(t)= 3t-5t+3 belongs to span S. b)…

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Q: Consider the problem min a2 – (21 – 2)³ + 3 subject to a2 >1 Which is the value of u*?

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Q: 4) The curver= V1 + sin20,

A: Solution :-

Q: 1. Solve by using the method of Laplace transforms: y" – 6y' + 5y = 3e¬*;y(0) = 2;y'(0) = 3

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Q: Transform to normal form and solve (showing the details!) 41. uzz + 2uzy + Uyy = 0

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Q: Consider the double integral xy I dA x2 + y? R. where R is the region of the XY plane, given in the…

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Q: Consider the curve C of equation (2x² – y + y³)² = a² + y? From the choices given, select the one…

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Q: 5. (D³ – 2D + 4)y = 0 ; y = – 2 , Dy = 8, D²y = 0, when x = 0.

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Q: Consider the solid Q bounded by the surface of equation y = x² + z? and the planes zV3 = x , x = 0,…

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Q: fined the genral solution 8) (D + D,)u = o

A: Solution of the homogeneous partial differential.

Q: Find the intervals of concavity and inflection ints of f. Sketch the graph of f.

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Q: let t={usx8 x-uiscoantableiuioi then Tis called Tcof

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Q: The function x2 f(x) = 1 - x is decreasing on (0, 1). Select one: O True O False

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Q: Subtraction in Arithmetic Modulo Determine if each of the following is a congruent modulo or not.…

A: To find given modulus substraction.

Q: 1241 + 245x2 + 35x3 + 24x4 = 24 %3D 356x + 24x2 + 35x3 + 75a4 = 2 24x1 + 56x2 + 35x3 + 67x4 = 47…

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Q: Consi der the lines : = 2 - y = z+1 and l2 : = y - 2 = 1. Determine a direction vectors for the…

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Q: Let n = pq where p and q are two distinct primes and consider Zn. Further, let [a] E Zn be an…

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Q: Consider the vector v = ( 5 1 -3) in R3. v belongs to Span{(( 2 -1 0), (1 2 -3)}. Select one: O True…

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Q: Mr. Smith decides to organize a potluck party with neighbors on a weekend. John Smith and his wife…

A: Every salad and every dessert should be considered as a different dish here.

Q: (c) Let M be the surface with the equation r³ +y³ +z = 9 that is above the right triangular region…

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Q: " + 4х 3D t + 4;B 2(0) 1, "'(0) %3D о

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Q: O to lusing a step size of 0.25 Solve the following problem over the interval from x = where y(0) =…

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