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Q: Q1. Find the general solution for the following differential equation: -y² (x²ex² - y²)dx+xydy=0

A: The given differential equation is; (x2e-y^2/x^2 -y2)dx + xydy=0.

Q: (dz) dt If (z=x. y), where x = cos (t) and y = sin (t) Q3. Use the chain rule method to find

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Q: 1.) dy dx 2x-y² 1+2yx = 0

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Q: Determine 4sin(x); the value of the arbitrary constants y(x) = C₁e* + c₂e¯* + y(0) = 1, y'(0) = -1…

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Q: 2. Are the planes 2x-y-4z = 10 and x - 2y + z = 4 parallel or orthogonal?

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Q: In the following exercises, compute the antiderivative using appropriate substitutions, and state…

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Q: a. Use the definition mtan lim x→a f(x)= b. Determine an equation of the tangent line at P. c. Plot…

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Q: Given that f(x)= x² + 5x and g(x) = x -2, find the unsimplified AND simplified versions of the…

A: f(x)=x2+5xg(x)=x-2

Q: B: use Lagrange interpolation formula to determine the relationship between the force and velocity…

A: By using Lagrange interpolation formula to determine the relationship between the force and velocity…

Q: 3. EVALUATE EACH OF THE FOLLOWING: A. 23 X (31-4²) =

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Q: f(x)-f(a) x-a a. Use the definition mtan = lim x→a a. mtan to find the slope of the line tangent to…

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Q: 1. 2x - 1 2x - 3 X x + 1 2x + 1 2x² - x - 3 = 0

A: Given equation:- 2x-12x-3-xx+1-2x+12x2-x-3=0

Q: Determine the complete solution for the following differential equation: y"+y+0.25y=0 if y(x) = y(0)…

A: For a second-order differential function, the characteristic equation will have two roots D1 and D2…

Q: Which of the following equations is a linear differential equation? (choose all possible answer) A B…

A: A differential equation is called linear if the equation is free from the product of dependent…

Q: The height of a straight circular cone measures 15 cm and decreases at a rate of 0.2 cm/min. The…

A: Volume of cone V=13πr2h Differentiating with respect to t…

Q: Determine the degree of the differential equati 3/2 2/3 (3x² ² 2 + 4xy) ¹ ² = (2y³d² - 4xy)" d²y dx²…

A: The given differential equation is; (3x2d2y/dx2 +4xy)3/2=(2y3d3y/dx3-4xy)2/3

Q: lim X-→-4+ lim X→→-4² 4x + [[4-x]] 2 3x² + 8x-16 4x + [[ 4-x]] 2 3x² + 8x-16

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Q: ← Find f'(t) if f(t) = -4t² +9t+3. f'(t) = K

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Q: Find the horizontal asymptotes of f(x) = √15x4-2 2x²-3 (Use symbolic notation and fractions where…

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Q: aquar the aquarium. (Use Show how to approximate the required work (in J) by a Riemann sum. (Let x…

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Q: ood to go Evaluate the integrals S√4x²dx 2. S 1 (4+x²)² dx

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Q: Identify the inside function, u = g(x), and the outside function, y = f(u). y = (x2 – 5x + 7)2 u =…

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Q: 1. For the function y = 5x³ - 4x a. Determine the average rate of change between x₁ = 3 and x₂ = 5.…

A: For the function y=5x3-4xa To determine the avarage rate of change between x1=3 and x2=5.b To…

Q: Find the derivative of the function. 2(5x² + 6x) 73√√x y' = y =

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Q: 10. 2/3 5² √4-9x² dx

A: As per our guidelines we are suppose to answer only one question, kindly rest can be reposted.…

Q: Find the solution of the DE (cos(x) + xcos(t))dt + (sin(t) – tsin(x))dx = 0 a. tcos(x) + xsin(t) = c…

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Q: A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s²…

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Q: 9. x², Let f(x)=sin(x), x < 0 0≤x<π/2 x-π/2, x≥π/2 (a) Graph f. Your graph should be accurate with…

A: See this solution in below.

Q: Find the antiderivative F(x) that satisfies the given condition. dF dx = -5ex - 4x; F(0) : = -9

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Q: 4. A. Find the parametric and Cartesian equations of the line connecting the points A (1, 2, -1) and…

A: Given two points are A(1,2,-1)   and B(-1,0,1). The cartesian equation of a line passing through two…

Q: Find  f '(a). f(x) =    square root of 1 − 2x

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Q: 01.Given f(x, y) = eªy(xy + x), show that fyy(x, y) — xfy(x, y) = x²exy

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Q: lim X> +∞o ( √9x² -5x+1 + 3x

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Q: Solve the given linear differential equation.Use C as the constant of integration in your solution.…

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Q: Prove that (x₁, y₁), (x2, y₂), and (x3, Y3) are collinear points if and only if X1 Y1 1 2 Y2 3 y3 1…

A: The given points are:   x1, y1,  x2, y2  and  x3, y3

Q: 5. A culture contains some bacteria, with the population increasing exponentially. The culture…

A: Let's find bacteria function.

Q: Show all necessary solutions and box all final answers. √√x² +11-3 x 4 3x²8x - 16° 1. Evaluate lim

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Q: A. FUNCTIONS, LIMITS AND CONTINUITY 1. For the function f(x) = 3× find f(x+1)/f(x-2). *

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Q: Find the equation of the tangent line to the curve y=8sinx at the point (π/6,4). The equation of…

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Q: A circular walkway is to be built around a monument, with the monument as the center. The distance…

A: Let's find equation of boundary layers.

Q: Pl-8] state the order, degree & Linear/ non-Linear DE. and identify as form, differential form? Q1…

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Q: Given that f(x) = 2x + 5 and g(x)= x² + 5, find: a) f(g(2))- b) g(f(2))- c) f(f(2))- d) g(g(2))-

A: We need to find composite function.

Q: 199. Let f(x) = cotx. Determine the points on the graph of f for 0 < x < 2 where the tangent line(s)…

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Q: Find the solution of the differential equation y" — xy' + y = 0 a. y = x² b. y = x c. y = 1-x² d. y…

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Q: 1. 2x - 1 2x - 3 X x+1 2x + 1 2x² - x - 3 = 0

A: We can solve the given equation by using the cross multiplication method.

Q: 8. Each of the following points is given in rectangulr (x, y, z), cylindrical (r,0, z) or spherical…

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Q: Q2. Determine the complete solution for the following differential equation: y"+y'+0.25y=0 if y(x) =…

A: y''+y'+0.25y=0 let y=emx y'=memx    ;   y''=m2emx…

Q: 3 5 -2 4

A: We can find the answer in the below steps.

Q: Let y=e¯*(Acos(x) + Bsin(x)) be the solution of the initial value problem for the differential…

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Q: Let y=e¯*(Acos(x) + Bsin(x)) be the solution of the initial value problem for the differential…

A: As 'y' is the solution of the differential equation , so it satisfied the given initial conditions.