The vector space C[a, b] of all continuous real-valued functions on [a, b] is not the span of any finite set. True False

Q: Evaluate: 3 Sy 21-2² dydz √x² + y²

A: The bounds of x and y are given below x3<y<2x-x2 and 0<x<3/2 y<2x-x2⇒…

Q: Evaluate: S ○ (2-√2) T 8 O (2-√2) T 4 O (√2-2) T 4 O (√2-2) T 8 16 sin √²+y² dady -y² sin [x² + y²

A: Option (B) is correct option.

Q: Determine the cube roots of = (1+j3)(2-j)

A: Given complex number is z=(1+3i)(2-i)                     (1) taking log of both side lnz=(2-i)…

Q: Provide an example of the following and explain why it works: 1.) A Galois extension of Q with…

A: Introduction: The Galois group of a certain kind of field extension is a particular group connected…

Q: Evaluate: ₁ da 2√x+3 ○1-3 ln (7/5) O2-3 In (7/5) 2 O2+3 ln7 03-In ()

A: Solution: To Find: ∫14dx2x+3

Q: Find d3f where f(x, y, z) = ln(x + y − z) + cos(x2y)

A: As per the question we are given a multivariate function as : f(x, y, z) = ln(x + y − z) + cos(x2y)…

Q: π/2 The integral f/² Scos sin drde is equal to O-1/2 O 1/2 01 00 10

A: We have to find the integral ∫0π2∫cosθ1sinθ drdθ .

Q: A region is bounded by the curve y = √2- and the lines y=-x and the x-axis. The integral expression…

A: We have to find the integral expression for the area of the region bounded by the curves y=2-x and…

Q: E be a subset of a normed space X and Y = Span E and a € X. Show that Let a € Ỹ if and only if f(a)…

A: To find: a∈Y¯, and f(a) = 0 whenever f∈Xι and f is 0 everywhere on E.

Q: Ju 20²u c² of2 (r, t) = u(x,0) = 0, ut(x,0) = 0 u(0,t) = 0 u(1,t) = 0. da2(x, t) + XX , 00,

A: Introduction: The basic method to solve a partial differential equation is the method of separation…

Q: a) b) Consider the following system of linear equations 2 P₂ -4 2 P -4 P as Given h=0.5, f₁=²-2i,…

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Q: 1.) Consider f(x) = 2x¹ − 5x³ + 1 for xo = 0, x₁ = 0.25, x₂ = 0.5, x3 = 0.75, x4 = 1.0. Calculate…

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Q: 10. Let A be a proper subset of N (set of all natural numbers). Then, A cannot be equinumerous with…

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Q: Using matrix algebra techniques, find a general solution to the system. 3x-8y y' = 8x-31y x(t) y(t)…

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Q: Show that if a non-zero element in a normed space X, then there is a bounded linear functional f on…

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Q: Consider the two differential equations: I: (4x + 3y²)dx + 2xydy = 0 2y II: (x²+²x) dx + (In x² −…

A: Exact Differential equation:      "The given differential equation of the form…

Q: dz Evaluate: ¹5 10+2 01 O Divergent 00 O-1

A:

Q: Find the solution of the given initial value problem y" + 12y' = 0, y(0) = −15, y'(0) = 12. NOTE:…

A: We have to solve the given problem.

Q: Given the matrix 123 A = 1 -1 0 0 1 2 a) By using the elementary row operations transform (A|I3) ⇒…

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Q: a) Find the domain of f. b) Find lim (x,y) →→(0,0) f(x, y) = zye 5210-26y f(x, y) or show that it…

A: We have to solve the following questions.... 1. We have to find domain 2.we have to show that limit…

Q: Inx S₁ Sox e-ey 0 1 dydx.

A:

Q: Determine ¹{F}. 4s+6 2 S+4s+4 SF(s)-2F(s)=-

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Q: Find the number zeroes with which the decimal representation of 700! terminates. a (a) 245 O (b) 199…

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Q: A chemist has three different acid solutions. The first acid solution contains 15 % acid, the second…

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Q: Bob, Trinity, and Roger are painting their living room. Trinity takes twice the number of hours that…

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Q: It is given that a smooth function F(x, y, z) of three variables have a gradient of (1,2,-2) at the…

A: As per the question we are given a function in 3 variables as F(x, y, z) whose gradient vector at…

Q: Add the following Mayan numerals together. Make any necessary exchanges and show all steps. It's a…

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Q: The solution of the following Bernoulli's equation xy' + 2y = x¹(cos x) y² is

A: The correct answer is not given in options.The solution with the correct answer is given as

Q: Evaluate √1 + x² dx dy ○ 2/3 ○ 2√2 3 O −1+2√2 3 O 1/3 8

A:

Q: Evaluate: S 10-11 O 2y+3 (y-1)(³-1) – In y − 1 − -dy − m¸|- -- ( y − 1)³ + - (y − 1)³ + In|y² + y +…

A: Follow the steps.

Q: Question a) b) 2xy Consider the function f(x, y) = 4x²+5² Find the domain of f. Show that the limit…

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Q: Consider the two differential equations: I: (4x + 3y²)dx + 2xydy = 0 II: (x² + 2x) dx + (In x² −…

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Q: Show that - dx /x²+2x+2 L- In(√5-2).

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Q: Give an example to show that X' need not be separable if X is separable.

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Q: Question 2 Given the function of two variables f(x, y) = (x - 9)² In² (y + 8)-(8x +9y)². Find all…

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Q: g) Determine length of the curve r(t) = 2cost î+ 2sint j + 3t k from (2,0,0) to (2,0,67)

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Q: Q5 a) b) (x > 0,k > 0) Find the Fourier cosine integral of f(x) = e-kx Find the Fourier series of…

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Q: 6 Evaluate 25 ○ In O Divergent ○ In 11 ○ 6 In 11

A: We know that , Improper integral of first kind can be represented as , ∫a∞ fxdx. Let , I = ∫6∞ 6dxx2…

Q: A y=1 x=y² B y=x² C (11) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1, and…

A: Given: Three regions A, B and C defined as: where region A is bounded by the parabola x=y2 and the…

Q: Find the maximum value that f(x, y, z) = x² + 8y - z² can have on the line of intersection of the…

A: Given function is f(x,y,z)=x2+8y-z2 and the other constraints are g(x,y,z)=2x-yh(x,y,z)=y+3z We…

Q: Which of the following differential equations are separable? dy (1)(1+2y²) = y cos x (ii) (e* +…

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Q: 7. x' = 1 1 2 1 -1 -8 -5 -3 X

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Q: (a) Given w = √3-i, (i) express w in polar form. (ii) find all the roots of 25 = √3-i in polar form.…

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Q: (b) Use the adjoint method to obtain the inverse matrix of P and hence. solve the system of linear…

A: Introduction: The transposition of the cofactor matrix for a given matrix is known as the adjoint of…

Q: .Let A= 10 1 1 1 -1 -1 1 O Solve the system Ax=(1 1 1) using the results of part (a).

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Q: Application - Social Media A vlogger receives a notification each day of how many views their vlog…

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Q: of R4. Create a basis for U. Consider the subspace X = U = = span{ 2 B 1 08- ‚x}

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Q: 7. Perform least squares on the following inconsistent system (Ax-b) by solving for using the normal…

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Q: Solve the given initial value problem. 6 19] -2 64 -[*]. 46 x'(t)= x(t), x(0)=

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Q: If A, B, and C are 3×3 matrices; and det(A) = -1, det(B) = 4, and det(C) = 3 then compute:…

A: We know properties of determinant for n×n matrices A, B…