If a, b, c are positive real numbers. Then prove that (a + 1)(b + 1) (c + 1)² >77 abct.

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A: Solution of the differential equations , using Laptop translation

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Q: (a) 64.

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Q: 4.2 Riemann Sums 103. Use a left Riemann sum with n 4 subintervals to approximate the area under the…

A: Note: "As you can't able to read previous answer so i answered here in handwritten."

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Q: 5) Find the divergence of (√x² +y + Z ¯) (î + y} + zk)

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Q: Find the sum of the series ∞ n=1 n+1 (-1)" 4 n accurate to three decimal places.

A: We have to find the sum of the series ∑n=1∞ (-1)n+1n4 accurate to three decimal places.

Q: Question 28 Evaluate. The differential is exact. (π, π, π) (0, 0, 0) O -2 02 O 0 0 1 -2 sin x cos x…

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Q: ILLUSTRATION 4.58 Find the equation of the plane which contains the line of intersection of the…

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Q: Classify the folowing ODEs as separable, exact, linear, homogeneous or Bernoulli. Some equations may…

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Q: 44 If 2x=y¹5+y-1/5, then express y as an explicit dy = 25 y. +x. dx function of x and prove that (x²…

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Q: 43 If y³ - y = 2x, then prove 1\d²y 27 dx 2 Hence, show that x 2 that +x. d²y dx² dy_1 = y. dx 9 24y…

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Q: Let L₁ be the line parametrized by (4-2t, 2-t, 3+t). Let L₂ be the line parallel to L₁ going through…

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Q: Let0<A;<πfori=1,2,...,n. that sin A₁ + sin A₂+...+ sin A,, ≤ n sin Use mathematical induction to…

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Q: .1) following transformations: a) x − ¹ {\ c). (s+2) s(s-3) = b) L{^(3-2e-3t)²}= s+5 (S-1)²+9 ? -…

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Q: The sum of n terms of two arithmetic progressions are in the ratio 5n +4 : 9n + 6. Find the ratio of…

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Q: Find the potential function f for the field F. Here you can assume that the vector field is…

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Q: 3. Find an orthonormal basis of the range of the following matrix: Show your work in details. 1 -1 2…

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Q: For the following questions, find a projection matrix P that projects b onto the column space of A,…

A: Given:  (i) A=100010001000 , b=1234 (ii) A=1-241-11111124 , b=1110 To find: We have to find a…

Q: For a matrix A: -101 0 0 0 10-1 Find the orthogonal complement of Im (TA)

A: Orthogonal complement of the space

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Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x³i + y³j+z³k out…

A: Given : F→x, y, z=x3i+y3j+z3k x2+y2≤4, 0≤z≤3 To find: ∬S F→ ·dA→

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Q: + tan dy 37 Ify = tan -1 -1 1 2 x +5x+7 1 2 1 2 1 2 x² + x + 1 +... to n term.

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Q: If * represents convolution, determine the Laplace transform of f(t) = 12t * e-3t

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Q: Question B: Test for the convergence 1. ΣΚ ki+k+3 2. Σκ=1 3k2+1 3. Σ cos(a.) given that Σ=zak = 1

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Q: z = sinh-15ej2

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Q: Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C…

A: We can find the integral by using Green's Theorem.

Q: Hi, this is the circulation solution. The question is asking for the flux? This should be the…

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Q: Consider the following linear programming problem: Max Z=12 x₁ + 15 x2 s.t. 20 x₁ + 10 x₂ ≤ 60 X₁ +…

A: Here corner points are , (0,0), (0,3),(3,0),(2,2) At (2,2) we have optimal solution.

Q: 4. Consider the Cubic Equation: x³ +3x² = 8x +30 a. Reduce the cubic equation through a change of…

A: The given cubic equation x3+3x2=8x+30 can be rearranged to the standard form as: x3+3x2-8x-30=0 A…