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Q: Solve the given differential equation. All solutions should be found. dy 3x² - 4y - y³ = dx 4x +…

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Q: 12. Calculate the area of the segment cut from the curve y = x (3-x) by the line y = x. A. 5/3 sq.…

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Q: Find y'. tan(x + y) = x + y

A: Solution ) tan ( x + y ) = (x + y ) Differentiate with respect to x d/dx tan ( x + y ) = d/dx ( x +…

Q: Solve the given differential equation by separation of variables. dp = P - p² dt et+c P = _t+c X

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Q: 3. A point P(3,0,5) lies on a plane that can be defined by the scalar equation Ax+By+Cz+ D = 0. A…

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Q: Find an equation for the level surface of the function through a given point. x-y + 2z (1,0, -1)…

A: Concept: Level surfaces: For a function, w=f(x,y,z):U⊆R3→Rw=f(x,y,z):U⊆R3→R the level surface of…

Q: Give the general equation of the plane containing the point (3,-1,4) and perpendicular to the line =…

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Q: Given a function, Based on the function, S-3 F(s) = 2 S² +6s+13 a) Determine ƒ(t). b) Based on…

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Q: d.w. Find the lengths for the - r = 1 + cosa

A: Given: r=1+cosθ

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: The given differential equation,      2y'+y=7t2

Q: x-2x +x= 15; x (0) = 7, x (0) = -16 hand written plz

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Q: If, in a monopoly market, the demand function for a product is p = 150 − 0.10x and the revenue…

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: dx 10) √x²4(14+x²) a) - - - c) - 1 4X ㅗ 4x + 1 andan ²/3 + c autan 1/2/3 + c 8 I ondan 2/2 + c 8 j 8

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Q: or what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable.…

A: For horizontal tangent slope y' = 0

Q: Which one of the following is the gradient of the tangent line at the point (6, -3) on the graph of,…

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Q: 2 X * sin² Lys y dy d

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Q: Show that the following series is divergent using the Test for Divergence. 4k³ - 1 k³ + 5k² + k k=1

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Q: Determine the values of b and c such that the function is continuous on the entire real line. f(x) =…

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Q: Q.2)(A) Find a formula for the area of the triangle in the xy-plane with vertices at A(0, 0), B(a₁,…

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Q: A rational inequality of the form R(z) <0 gives the number line below. What is the solution of the…

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Q: 8-9 Let A = 2 3 (a) Find 5A +6B. 5A +6B = and B= 9-2 Complete parts a through d.

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Q: C

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Q: السؤال الثالث Question Three * Q3. For the motion vector r(t) = et cost i + et sint j , find: (i) N…

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Q: A farmer has 400 yards of fencing and wishes to fence three sides of a rectangular field (the fourth…

A: A farmer has 400 yards of fencing and wishes to fence three sides of a rectangular field.

Q: Use the chain rule to find the indicated partial derivatives. Əy ar Əy əs Əy at II Y = w tan-¹(uv),…

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Q: Given f(x, y, z) = ze™" - a sin none of the choices 02-1/ 02²/ 0 01- ¹(), what is fax (0,2,1)?

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Q: Solve the given differential equation. All solutions should be found. dy 3x² - 7y - y³ = dx 7x +…

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Q: The equation of a surface in spherical coordinates is given by p= 6. Rewrite this equation in…

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Q: 8 -9 9 -2 LOMA- [2 ²3] and B-[37] Let = B= 1 (a) Find 5A + 6B. 94-57 5A +6B = 28 21 (b) Find 6A-5B.…

A: Addition and subtraction of Matrices

Q: ki a) limx→∞ f (x) = b) limx-f(x) = c) limx-of (x) = d) limx-3f(x) =

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Q: 9-1² 9-1²-² 1.****** (a) 1 dz dy da Sketch each of the following: . the solid E • the projection of…

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Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

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Q: Find the solution of the given initial value problem. πT ty' + 2y = sint, y = 3, t > 0 Y ||

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Q: 1. Determine whether the series n=1 3n+1 ln(n+1) is convergent or divergent.

A: : since,1&lt; ln(n+1),for n&gt;2 so, 0&lt;(n^2)/(((3^(n+1))*ln(n+1))&lt;n^2/n^4=1/n^2,  since…

Q: Instruction: Evaluate the following Integrals. Write your COMPLETE solutions neatly and organized.…

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Q: Find an explicit solution of the given initial-value problem. 없을 y(7) = 7 1

A: Find an explicit solution of the given initial-value problem.         dydx=y2-1x2-1  ,    y7=7

Q: Solve the equation. Approximate the solution to four decimal places. e5 — 3x = 10

A: We can Tak ln both side and solve as follows

Q: Solve the following system of linear equations: X₂-5x₂+x3 = 2 If the system has infinitely many…

A: The given system of equations,        x1-5x2+x3=2

Q: Given lim (x,y)→(1,2) of  (x + y − 3) / (x^2 − 1) Evaluate the limit along the paths y = 2 and y = x…

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Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: Trapezoidal rule:-∫abf(x)dx=∆x2{f(x0)+2f(x1)+2f(x2)+...+2f(xn-1)+f(xn)}where ∆x=b-an, n is the…

Q: 5. 1-cos2y 1+cos2y dy

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Q: The value of n when integrating the following function using Simpson's method is: [2²/ dx h = 0.2 >

A: solution is given below

Q: Q3) find the soluation of differention equation 1) 2y' = y cot(x)

A: To find the solution of the differential equation 2y'=y cot(x) Formulae used : ∫dxx=ln |x|∫cot(x)=ln…

Q: The following limit gives the derivative of a function f(x) at a point xo: lim h→0 (2+h)³-8 h -8)…

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Q: Find y' y = 5x² + a4

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Q: Find dy dx 2 for x²exy = 5 WA/

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Q: Evaluate S 2 dx √x4+25

A: ∫1au+b du = 1alnau+b+C

Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i-2j+ 2k. 1, Find the unit vector…

A: We can solve this as follows:

Q: Q6) Test the convergence of the following n! 2) En=1 (2n+1)!

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