Identify the surfaces of the following equations by converting them into equations in the Cartesian form. Show your complete solutions. (a) z² = 4 + 4r² (b) p = sin o sin

Q: = xe²* is a solution to y' + ay — e²x = 0... 3. Find the constant a so that (x) = xe² 04 3 O 1 O -1…

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Q: 4. Let f(x)=√√2 cosx - x (a) Determine the absolute extrema of the function f on the interval [플,플]

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: 4. Solve the trigonometric identity: sin4x = 2sin2xcos2x.

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Q: I. Evaluate the following limits. sinh r x² 1. lim r→0 sinhr — –r

A: Given that limx→∞sinhx2-x2sinhx-x

Q: ди 2х + ди วง =0, 4 (0,y) = зегу u

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Q: 5. The state-space representation for 2x" + 4x + 5x = 10e" is D = +² го 98

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Q: Evaluate J by means of trapezoidal rule using n = 10 and n = 20: 1 J = exp(-x²)dx = Se

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Q: Determine the values of r for which the differential equation y" - 36y = 0 has solutions of the form…

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: 9. Two swings are hanging from a 3 meter rectangular wood beam embedded at both ends. Swing 1 is…

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Q: Use the method of separation of variables to solve the bo

A: Given,           ∂u∂x+∂u∂y=0,                               ...(1)    u(0, y)=3e2y…

Q: Evaluate J by means of trapezoidal rule using n = 10 and n =20: 1 = [*exp(-x²) dx Evaluate J by…

A: We need to find the value of J=∫01exp(-x2) dx using the trapezoidal rule with n=20 and n=10

Q: 4. Evaluate the double integral: Loddy. dx dy. +1 (Hint: Change the order of integration to dy dx.)

A: ∫08∫y1/32yx7+1dxdy limit of x goes from x =y1/3 to y =2 and limit of y goes from y = 0 to y = 8 on…

Q: VI. Determine the instantaneous rate of change of the function 2 f(x) = ² Love √x sin (³) dt 1+√t 10…

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Q: Determine L-1 1 s²-3s-4 (s-3)(s-1)².

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Q: Let v1 = (1,2,1), v2 = (2,9,0), v3 = (3,3,4) . Show first that S= {v1, v2, v3} is a basis for ℝ^3.…

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Q: (c) (i) Give a necessary and sufficient condition for the differential equation M(x, y)dx + N(x,…

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Q: 20. Find the volume of the parallelepiped with adjacent edges u = (-2, 0.75, 4), v = (6, -0.3, 8),…

A: Solution :

Q: Using the Rodriguez formula obtain the Legendre polynomials Pn(x) for n=0,1,2,3,4,5

A: We have to find the Legendre polynomial Pnx by using  Rodriguez formula for n=0, 1, 2, 3, 4, 5. The…

Q: A rhombus has sides that measure 4ft. each. If its smaller angle measures 40°,how long would be the…

A: For a rhombus, the diagonals are: The angle bisectors. Perpendicular to each other. Bisect each…

Q: 10 2 12 ch 16 9 12 13 16 Graph 2 For Items 49-52. Refer to Graph 2 51. Which of the following edges…

A: given graph,

Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x,y) =…

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Q: 3. Prove that if G is an open set dense in the metric space (S, d) then SG is nowhere dense in S.

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Q: Question 4 a) Soive DE 11 —y"+y² + y = o b) -15

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Q: 17. Given the following degree of the vertices of an undirected graph H= {4,1,5,3,4,3}, we can…

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Q: (ii) Show that the set of solutions {₁, 2} is a fundamental set of solutions. (iii) Hence, or…

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Q: Solve the system by Gauss-Jordan Elimination

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Q: 16. A cruise ship's path travels for 16.1 miles at an angle of 60.3°. It then follows a path that…

A: Given a cruise ship's path travels for 16.1 miles at an angle of 60.3°. It then follows a path that…

Q: (b) Let f and g be contraction functions with common domain R. Prove that (i) The composite function…

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Q: the following problems completely. 1. Use local linear approximation to estimate √√(3. 95)³

A: Given f(x)= sqrt(3.95^3) We need to find L(x) Where L(x) is the linear approximation

Q: Evaluate the double integral: 8 So Son 27 4+1 de dy. dx 1/3 Hint: Change the order of integration to…

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Q: 9. The inverse of an element a of Z under the operation * defined as a*b = a + b - 1 is A. a -2 C.…

A: Solution :  Options (B) is correct

Q: 2. lim (x - Inx)* +0+x

A: Given that limx→0+x-ln xx We can write it as limx→0+elnx-ln xx=limx→0+exlnx-ln x

Q: 6.2x2y=6 x=y+z=1 3y2z=-5

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Q: Sketch f(t) and find the Laplace Transformation of the following functions. e2(1-s)n-1 1. f(t) =…

A: The given problem is to sketch the given periodic function and find the Laplace transformation of…

Q: Q3) Solve the following boundary value problem using finite difference method d²y dy given that 3- +…

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Q: Let A ∈ (R) be given If A is nonsingular, prove that adj(A) is nonsingular and adj(A)^-1 = (A^-1)

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Q: Q.2. The side of a cube is measured with a possible percentage error of ±2%. Use differentials to…

A: Given that the sides of a cube is measured with a possible percentage error of ±2%. We have to…

Q: Find the volumes of the solids generated by revolving the shaded regions in Exercises about the…

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Q: Consider the following second order differential equation y" - 4y + 8y = f(x) 1. Find the solution…

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Q: 9. The inverse of an element a of Z under the operation * defined as a*b = a + b - 1 is A. a - 2 C.…

A: Solution :  Options (B) is correct

Q: Evaluate J by means of Simpon's rule using n = 2m = 10 and h = 0.05. Reminder that the integral…

A: Answer is = 0.7468

Q: 38. Which of the following nodes should be the root of Tree A so that nodes B and I will be of the…

A: 38

Q: (a) Determine whether the set of functions is linearly independent on the interval (-∞, ∞). f₁(x) =…

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Q: Which of the following operations is associative on Z? A. a*b = a b C. a*b = a B. a*b = max (a, b)…

A: Solution :

Q: Determine the convolution of the following signals using z-transform: x,(n)=(¦;}'u(n-1),…

A: We can solve using   z-transform

Q: Question 6 obtain the power Series solution of the IE V" - (1+x) y = 0 about the ordinary point x =…

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Q: 13 2 1 Given A = 2 13 3, find wwww 4 2 1] the lower triangular matrix. [3 0 0 a. 2-1/3 0 C. [4 −2/3…

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Q: (b) Consider the 2nd order linear differential equation xy" + y = 0. (i) Given that y₁ = ln x solves…

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Q: 3. Imagine you fill your bathtub up at a rate of 2 gallons per minute. This means that every minute…

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Q: 43.Given that Tree A is bipartite, which of the following gives the grouping of the vertices of Tree…

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