2. Compute [²√x by first changing it to polar coordinates. 1 -√3x (x² + y²) ² dy dx

Q: 5) An equation of the of the plane passing through the points P(0,2,1), Q(2,1,2), and R(3,3,1).

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Q: Find an explicit solution of the given initial-value problem. dy_y²_ 1 = y(4) = 4 dx 1 ||

A: The objective of the question is determine solve the differential equation.

Q: An integral expression for the area of the surface generated by rotating the curve y=√x, 0≤x≤ 1…

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Q: Find the inverse of the following matrix by using Gauss-Jordan eliminations 1 21 -1 2 3 122₂ +1 0 41

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Q: Write the function in terms of unit step functions. Find the Laplace transform of the given…

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Q: 21. Find the solution of the given initial value problem. y’’+y’+1.25y=0,     y(0)=3, y’(0)=1…

A: NOTE: Refresh your page if you can't see any equations. . the auxiliary equation is given by

Q: Sketch the graph indicating maxima, minima, asymptotes and inflection points for the x² +1 function:…

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Q: Evaluate [(cos² 0 + 2 csc² 0 + sin²0) do. (a) 0 + 2 cot 0 +C (b) 0 2 cot 0 + C - (c) sin²0 + 2 cot 0…

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Q: Find the solution of the given initial value problem. y’’+4y’+5y=0,     y(0)=1, y’(0)=0

A: Initial value problem.

Q: Find the exact length of the curve. y = 9 + ¹ cosh (8x), 0≤x≤7

A: The curve y=9+18cosh8x, 0≤x≤7

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 & x=2rcos θ , y=2rsin θ

Q: Let g(x) = 2 f(u) + 3 where . u= u = with respect to x? ○ 2. f' (u) +3 O (2. f' (u) + 3) (2x + 2)…

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Q: Evaluate the definite integral. TT/3 [C [(sec t tan t)i + (tan t)j + (2 sin t cos t)k] dt 10

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Q: Q1. Find the inverse of the following matrix by using Gauss-Jordan eliminations 1 21 2 3 12₁₂ +1 -1…

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: Q3/ Evaluate: ff(x+y) dy dx for the region bounded by the x=0, x=2, y = x and y = x + 2

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Q: (b) In an oil refinery, a storage tank as shown in Figure 1 contains 2000 gal of gasoline that…

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Q: Which of the following is the result of differentiating both sides of the equation xsin y = 2 ln x +…

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Q: Solve the given differential equation. All solutions should be found. dy x8 - 6y dx X NOTE: Use c…

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Q: identify the equation of the curve that passes through the point (0, 1) and who tangent line has…

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Q: 8. Determine the area bounded by x = -y² + 4y and the y-axis.

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Q: 5 Qu/ If w=f(u, v) = cos uv, u = xyz , v = 4(x²+y²) dw Prove that 0 at the this point…

A: Given problem:-

Q: Use synthetic division to find the quotient and the remainder. (3x³+2x²-3x-15) + (x+2)

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Q: A cube with sides 14 inches long is covered with a coat of fiberglass 0.4 inch thick. Use…

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Q: Compute AB, where A AT B = = 24 09 4 -3 -1 and B = 76 (1 %). 6 4

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Q: 3. Which of the following is the most appropriate technique to use in evaluating (a) Integration…

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Q: Integrals question! Find the total area enclosed by the curve f(x)=x3 -4x and the x-axis, between…

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Q: Which of the following gives the area of the region bounded ㅠ by the curves y = sin x, y = sin(2x),…

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Q: If z = 24 - 2x - 6y, x = cos(4t), and y = esint, then dz dt is equal to O-2 sin(4t) - 6esint cost O…

A: Since you have posted multiple problems we will answer first problem for you for remaining problem…

Q: C. (à x b) .c

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Q: Find f'(x). f(x) = = O V 10x - sin²(7x) 1 f'(x) = = 2√/10 - 14cos(7x) 1 f(x) 2√10x - sin² (7x) 10…

A: This question is related to differentiation, We will solve it using given information.

Q: Solve the initial value problem y"+y=f(t), y(0)=y'(0) = 0, (21 2t if 0 1

A: Here is the solution of the given problem. We solve this problem by using Laplace transformation

Q: If integration using u-substitution technique is used to solve for O u = e4x Ou=1-e¹ O U= u = €²x…

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Q: A management company is going to build a new apartment complex. They know that if the complex…

A: To find the number of apartments for which the cost is minimum and also find the minimum cost.

Q: Q3) Find the integration by using Partial fraction method Y x² + 2x + 1 (x² + 1)² dx

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Q: Find the value of an investment of $25,000 for 13 years at an annual interest rate of 3.15%…

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Q: The definite integral that will give the area of the region R using VERTICAL strips is +2 ° ³* ((2²…

A: Explanation of the answer is as follows

Q: State the order of the given ordinary differential equation. (1-x)y" - 4xy' + 6y = cos x Determine…

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Q: Apply

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Q: 10. Show that these two lines are coincident. [x, y, z]= [1, 5, -2]+s[1, 7, -3] [x, y, z]=[-3, -23,…

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Q: Which of the following conditions is NOT required for lim f(x) to exist? x→a

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Q: If integration using u-substitution technique is used to solve for ∫2e2x1−e4x dx/square root of…

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Q: (b) Given that s² + 16 (S-1)(s+3)(s²+4) Evaluate the values of A, B, C and D. A B Cs + D (s-1) (s+3)…

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Q: 6 5 4 1 -7-6-5-4-3-2-1, 1 2 3 4 5 6 7 -3. -6 147

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Q: Find the equation of the tangent line to the curve y = 3 sec(z) - 6 cos(x) at the point (π/3, 3).…

A: The equation of tangent line

Q: 1.) Sales of a particular product have been declining continuously at a rate of 8% each year. a.…

A: We need to find D.E. As per Bartleby's guidelines we can solve 1 question from multiple qn. Please…

Q: Q6) Determine if the following integrals converge or diverge. If the integral converges determine…

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Q: 3. 2 cos¹ √x = cos ¹(2x-1) 0≤x≤1

A: We have to find out

Q: If f(x) = 6 sin¯¹(x²), find ƒ'(x). Find ƒ'(0.5).

A: This question is related to differentiation, We will solve it using given using given information.

Q: Determine whether the series converges. The series 8 k=1 13 15k

A: