Use the Midpoint Rule with m = n = 2 to estimate the value for 4x + 2ydA on the rectangle R = [0, 8] × [0, 2]

Q: Find the distance between the planes 5x − 3y + z = 2 and 5x − 3y + z = −3

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Q: Show that the square of the length of subtangent at any point on the curve by2=(x+a)2 (b is not…

A: Here given curve  by2=x+a2

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

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Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approxim

A: Given,         f(x, y)=11-2x-y

Q: Ex: Find the distance between the pt G(4₁-4,4) and the line x=2t₁ y=Z-3, z = at +2₂

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Q: Find the points on the cone z² = x² + y² that are closest to the point (-5,4,0)

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Q: Y is the midpoint of XZ and V is the midpoint of WZ. If VY = 32, what is WX? WX Submit

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Q: Find the average squared distance between the origin and the points on the paraboloid z = 4 – x² –…

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Q: Find the greatest and smallest values that the function f(x, y) = 4x+5y takes on the circle x2 + y?…

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Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: Use the trapezoidal rule with n = 5to estimate V7 + y³dy

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Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Use the Trapezoidal Rule with n=6 to approximate π∫0sin2xdx.

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Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 8x – 6y on the circle…

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Q: B) Use Lagrange multipliers to find the the points on the circle a² + y? = ry has its extreme…

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Q: Find the maximum value of f(x, y) = 3ry(9 – 45x – 9y) over the triangle with vertices (0,0), (,0)…

A: Maximum value occurs at critical points or on the boundaries of the triangle.

Q: Find the length of the curve. x = 413. y = 612. 0 sts v8 %3D The length of the curve x = 4t°, y = 6t…

A: Given curve x=4t3,   y=6t2    0≤t≤8

Q: The area bounded by the curve y3a and the lines z 4 and a-9 above the z-azis is aquare units O 27v0…

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Q: use the trapezoidal rule to approximate use n=6 and h=1

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Q: Find the extremum of f(x,y) = 9x2y² +4y² + 4x². %3D Answer:

A: Topic= Derivative the extremum is 0.

Q: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: Find the best quadratic approximation, Q(x, y) of V9 – 6x – 4y for (r, y) near (0,0).

A: We have to find the best quadratic approximation Q(x,y) for (x,y) near (0,0).

Q: (d) | (3+ecos (0 sd AX ·

A: As per your query the solution of the problem (a) has been done in midpoint rule. For the solution…

Q: Find the length of the curve y = In(1 – x), 0sxs.

A: Given: y=ln(1−x2)0≤x≤12

Q: Ue langrange multipliars to fined the Shortest distancé fam the to the pGine x+g+Z=1. point (7,0,)

A:

Q: Use the method of undeterminad Coefficiento to slve the initial valene proalem : yo +Qy'+5y=cin…

A: The given initial value problem is              y''+2y'+5y=e-tsin(2t)  , y(0)=1, y'(0)=0 We find the…

Q: Find the Felative Maximum vasve of Fx,x) = x*- y, Subuicct to the Construint X-Y=24.

A: The given function is as follows. fx,y=x2-7y2 the given constraint is as follows. x-y=24y=x-24 The…

Q: Find the points on the cone z 22 x2 + y? that are closest to the point (-5,2,0)

A: Aim: Find the points on the cone z² = x² + y2 that are closest to the point (-5,2,0).   Basic…

Q: wz bisects 2XZY and 2X = ZY . Which choice of method can be used to prove AXWZ = 4YWZ ?

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Q: Find the points on the cone z2 = x² + y² that are closest to the point (-2,2,0)

A:

Q: Find the distance from the x-axis to the plane z = 3.

A: Given equation of plane - z = 3z-3 = 0       ................(1)General equation of plane is given…

Q: Find the length of the the interval -2sxs-1. y = L, V3t² – 1 dt curve in

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Q: Find the points on the cone z 22 = x2 + y? that are closest to the point (-3,1,0)

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Q: find the distance between 4y+3x=4 and (0,5)

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Q: Find the best quadratic approximation, Q(r, y) of V9 – 6x – 4y for (r, y) (0,0). near

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Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

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Q: Find the line integral (4х — 5у) ds, where C is the semicircle y = 9 – x² traversed from (3,0) to…

A: Graph the semi-circle. Take x=3cost and y=3sint Now, x'=-3sint and y'=3cost The angle covered by…

Q: Show that the square of the length of subtangent at any point on the curve by =(x+a)°.(b÷0) varies…

A: We will prove it as following.

Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: The area bounded by the curve y = 6z and the lines a = 5 and z= 8 above the T aris is 234.00 square…

A:

Q: Use the method of Lagrange multipliers to maximize 2x + 3y – 4 on the circle x² + y? = 13

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Q: dx Calculate for n = 6, using trapezoidal rule. %3D -11+ x²

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Q: Find the Võlumé of thé šólid generated by revolving the shaded region about the given axi About the…

A: Explanation: If we rotate the shaded region about the x-axis, we will get the cone shape. Height of…

Q: Find the isogonal trajectories to a family of straight lines y= cx that cut the lines of the given…

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Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

A:

Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (Hint: To simplify the…

A:

Q: Calculate fSp(3x + 2y) dA where D is the region in the first quadrant that is inside the circle x2 +…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.