Evaluate the integral (t³ In ti+ 3t³ sin (t) j+k) dt.

Q: b). Using an appropriate triple integral, evaluate the volume of: [Verify using Mathematica] i).…

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Q: The number of computers sold per day at a local computer store, along with its corresponding…

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Q: c). Evaluate √√x² + y² ds along the curve r(t) = (4 cost)i + (4 sint)j +3tk, -2x≤t≤2π.

A: We solve the given line integral.

Q: F :1: Solve L-1)2(s+10)-140 섹 (s+1)² +400)

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Q: = Find the general solution of the following PDES. LO • з Их + 2 Иу ansg- и(x,y) = не , u(x,0) = чех…

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Q: Use iteration to guess an explicit formula for the sequence defined by an = an-1 + n for all…

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Q: 1. Find the inverse of A = 1 0 2 3 1 1 using the Gauss-Jordan method.

A: As per norms, we will be solving only one question. If you need an answer to others then kindly…

Q: Q5(a) Let f(x) be a periodic function with period 4 such that f(x) = {2; 0<x<2 2<x<4 (1) Find the…

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Q: 7. The coin is tossed twice. Which of the following is the correct representation of the sample…

A: ans 7  (a) {HH, HT,TH,TT} Ans 8 (d)   36 (6 into 6)

Q: in the firs dV= dz

A: Let us consider a triple integral of the form ∫ab∫f(x)g(x)∫h(x,y)r(x,y)F(x,y)dzdydx To solve the…

Q: Let p= "It is extremely humid." Let q= "It will rain tomorrow." Convert into symbols: a. "If it is…

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Q: 1. " Identify the surfaces of the following equations by converting them into equations in the…

A: As per the company guidelines i am solving first question please resubmit the question for another…

Q: Find the line integral along the given path C. f(x-y)d: - y)dx, where C: x=t, y=3t+8, for 0sts6…

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Q: Perform the following math operations to the given Matrices A- 0 2 L-24 B c= [1 2 -2] C= 0-1 O E= 2…

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Q: if f ofen mapp Prove that for every. xeX and for every ofen Set Vxe Tx in x contains the Point x…

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Q: 19. f(x, y, z) = x² + y² + 2², holds 2x + y + z = 1, -x + 2y3z = 4

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Q: Equation: f(x) = 5cos(x) + sin(x) - 2sec(x) Tolerance: x10-5 Assume x = 0.5 (in radian)

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Q: By Separation of variables, Solve the follow PDES :- ²4 d²4 dt² =43 2 dx² •o u(e,t) = u(s, t) =6…

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Q: Let a₁ = a₁ = a₂ = 2 and an = an-1 + an-2 + an-3 for n > 3. Prove, using strong ao mathematical…

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Q: Gaussian Elimination Equations: 3X1 - 2x2 + x3 = 4 2x1 - 5x3 = 1 -3x2 + x3 = -1

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Q: Q3: A Cummins diesel engine is available in heavy-duty pickup trucks. The probability of the engine…

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Q: Find the general Solution of the following PDES -Х • з Их + 2 Иу =0 ucx, c) = че 2 ans3- исх, у)…

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Q: 32. Model With Mathematics In order to take a panoramic photograph, a camera must have a hyperbolic…

A: From given data we can conclude that, By Standard equation of hyperbola :y2a2-x2b2=1

Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 4y = 3e³t Y(t) =

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Q: Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money, but…

A: Given that Ronnie goes to the racetrack with his buddies on a weekly basis.

Q: • Find the upper Riemann sum U(f, P) and the lower Riemann sum L(f, P) for each of the following…

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Q: Consider the paraboloid paremterized by o(u, v) = (u, v, u² + v²). 1. Find the second fundamental…

A: 1 Consider the paraboloid parameterized by σu,v=u,v,u2+v2. We have to find the second fundamental…

Q: a € ¹ { x² + 0²² 8² + 6² } s2 [sen (3t+ 2u) + sen(8u - 3t)] du Applying the Convolution Theorem to…

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Q: Theorems Let {xy and fyny betwo Se @ X n + Yn w X+Y в 2х ш> hx WheF

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Q: olve parts c

A: Given that the fish and game department in a certain state is planning to issue hunting permits to…

Q: m For fixed a, consider the quantity cos(x + h) Q(x, h) = a) What is the limit (x) of Q(x, h) as…

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Q: r² (t) = 2 + ₁ + (²² + 3)) + (2+² + 5) k 明 Find ICH and ÑA)

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Q: if (11 + 2! = d+ie), find the equation of 1+ 21 the ellipse whose Vertex is the origin and the one…

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Q: (b) Find for what value of the equation 12x²+36xy + y² + 6x + 6y + 3 = 0 represents a pair of…

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Q: 4. Solve the following 2nd_order OPES (5 steps) day = ( x ) = + (1 - 1) dy dx² dx h=0.02 Y(0) = 4 ال

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Q: 5. Use Cartesian coordinates to evaluate Jff v² av where D is the tetrahedron in the first octant…

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Q: Start with an unknown number. Triple it and then subtract 5. Now, take the new number and double it…

A: Let the original unknown number be x. Triple it and then subtract 5 :   3x-5 Take the new number and…

Q: □ classify the following PDES :- 227 822 82 -2 +2 =x+3y дх2 буду дуг • x Uxx - 2xy Иxy +y uyy = e…

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Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

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Q: By Separation of variables, Solve the followin PDES :- • Su d2u dx2 @ o dt U (0₂t) =(4,t) = o u…

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Q: rt - fe e2u f(u)du f(u)dut-

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Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

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Q: Solve the given system by: a. LU factorization b. Cramer's Rule 2 -4 1 -4 0 3 -1 0 1 -1 3 Show…

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Q: Use the inner product (p, q) = a b + a₁b₁ + a₂b₂ to find (p, q), ||pl|, |la||, and d(p, q) for the…

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Q: Find the complete solution of дz where p = x дz and qay pq = xy,.

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Q: Solve the following differential equations : X 2y + v² 2x (x² + 5)² dx + (x+y)dy = 0

A: First we will check if the given differential equation is exactly if it is not exactly then we will…

Q: (b) Show that the continuous image of compact set is compact but the convers need not to be true.…

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Q: 10. Write and simplify the integral that gives the arc length of the curve y = x³ +500 for -1 ≤ x ≤…

A: Consider the equation of the curve, y=x3+500 for -1≤x≤2. the arc length is defined by the formula,…

Q: D. Suppose p, q, r, s are propositions such that p^q is true and rv sis false. Determine the truth…

A: We know that,  A∧B is true if and only if both A and B true  A∨B is false if and only if both A and…

Q: Find the differential dz of the function f(x, y) = 4y²+x²y-2xy and use it to approximate Az at point…

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