6- Determine the domain of the function f(x, y) = In(x² + 2y² + 1) + arcsin Vx - 1 a) D = {(x, y)| 1

Q: a) Demonstrate Gra phically the contimuity /Discontinuity of the tunction fx)- * ,0くxく」 1. 1+x)…

A: Authoring guidelines:…

Q: 2) a) Ŝ find the value of the inter Specify the integrol liees |-x2

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Q: r cos(y) + y(e² - 1) x + 0 f (x, y) = ry x = 0.

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Q: Find the areas of the regions

A: Given that, The bounded area of the circle is given by

Q: b) Show that F - dr is independent of its path, given that y F(r, y, 2) = 1+. + tan-2) i+ tanrj+ k.…

A:

Q: 17. Evaluate the line integral xezds, where C is the line segment from (0,0,0) to (1, 2, 3).

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Q: Region bounded by y = x* +2, y = x+4 rotated about the x-aKis 2.

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Q: F(x,y) = (1+ 2xy?)î+ (2x°y +2y)}

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Q: Bounded by the cylinder x 2 + y 2 = 1 and the planes y= z x =0 z= 0 in the first octant

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Q: 8. The region in the first octant bounded by the coordinate planes, the plane y = 1 – x, and the…

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Q: Let R be the shaded region bounded by the parabola y = 4 - x², and the lines y = 1- 2x and y= -1, as…

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Q: 3 - Find the bounded ly y=2x-2, x=-1, x= 2 3 area y=2X - 2, x=-I, x= 2 4- Find the anea bondol .

A: Integrate the given parabola from x=-1 to x=2

Q: Suppose the closed curve C in R? starts at the point (-1,1), goes along the parabola y = x2 to the…

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Q: Po Prove that fcz) = zis coutinuous at z=z. O Prove that. fZキ2。 is dis continnity at z=Zo, where Zn

A: (1) we have to prove that                                                              f(z)=z2 is…

Q: It is easy to see that u(z) = Im (+) is harmonic in the unit disk |2| <1 and lim,→1- u(reio) = 0 for…

A: Given, Uz=Im1+z1-z2,z&lt;1 Now,…

Q: A clamped cubic spline S for a finction fis defined by a(x - 3) + (x-3)²+b(x – 3)³ - 2(x-4)-5(x -…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: All students are located at integral coordinates in the xy-plane. The x-coordinates belong to the…

A: Here we will use application of derivatives in finding slope to tangent and normal.

Q: 2. The region bounded by x = 2 y, x = 0, y = 9 is rotated about the y - axis.

A: Given Data: The given curve is x=2y. Rotated about y axis. The limit for y axis is (0, 9).

Q: 3 Find the abscissa of the centroid of the region between the parabola y = 9 − x2 and the line y…

A: Given :The parabola y=9-x2 and the line y=2-2x from x=0 to x=2.To find :The abscissa of the centroid…

Q: İki noktalı Gauss kareleme yöntemini kullanarak S dx integraline 1+16x4 yaklaşık değer bulunuz. 2…

A: we have given by integral ∫-12128x21+16x4dx we have to solve the integral by using two-point…

Q: A region in the xy-plane is bounded by y = 2x + 2, X = y + 2, y = -2, 2 y = 2. and

A: Given curves are y=2x+2 and x=y22+2 The limits are y=-2 and y=2 We isolate x from the first curve,…

Q: The path C is a line segment of length 10 in the plane starting at (1, 1). For f(x, y) = 6x + 8y,…

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Q: A region R consists of a square bounded by the lines x = -1, x = 1, y = 0, and y = -2 and a half…

A: The given region is as follows: The area of region is  A=∬RdA  =Area of semi-circle of radius…

Q: Let S be the portion of the cylinder z = 1 − x2, in the first octant and between the planes y = 0…

A: We will find out the required value of a.

Q: Sketch the region enclosed by the given curves. y = tan(7x), y = 2 sin(7x), -77/21 sxs 7/21 y y 3 3…

A: For sketching the region y=tan7x, y=2sin7x, -π21≤x≤π21. Let y1(x)=tan7x, y2(x)=2sin7x, -π21≤x≤π21 We…

Q: The area under the region bounded by the curve f(r) cos r, the a-ax and the lines x = %3D and a = 2…

A: From the given curves the bounded region is as shown below: Now taking the vertical strip, so the…

Q: 3. The region bounded by y = x³, y = x, x > 0 is rotated about the x – - axis.

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Q: 1.13 Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

A: The given function is x4dx+xydy By green's theorem, the integral becomes, ∫06∫06∂M∂y-∂N∂xdxdy where…

Q: Show that the function f defined on [0, 1] by the conditions f)=2rx when <,r=1, 2, 3,. 1 1=1, 2,…

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Q: 2. Integrate f(x, y) = sin /x2 + y² А. over the closed unit disk.

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Q: a) Plot a direction field and some integral curves  for xy'-2y=-1 on the rectangular region {-1<or…

A: a) given differential equation  xy'-2y=-1 claim- plot a direction field and sole integral curves for…

Q: line integral Compute the where part of the cirele x² +yR=9 C is the %3D in the first quarant from…

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Q: The region lying underneath the graph of f(x)=2x^3 over the interval [0,4] has centroid

A: given: f(x)=2x3     [0,4]

Q: f(2) = u(x, y) + jv(x, y) v(x, y) = sin x cosh y f (0) = 0.

A:

Q: Evaluate this integral Sc v – 2x)dy – (yx – x²)dx where C is a curve consisting of C, which is a…

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Q: The region is bounded by the curves y = x² and y = 4x - x² and is rotated about the line X = 4. %3D…

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Q: curve in the xy-plane is denned by the vector valued functic dy in terms of t? dx? where x(t) = 2…

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Q: Exercise 5 3x + ax + b x² +1 Conşider the function f that is defined over IR as: f(x) = Where a and…

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Q: Show that 1 y - X 1. Z-y X-Z = 1. %3D alx-y) alz - x)

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Q: Find the divergence of F(x, y, z) =(a -1 Y, y? + 1' 3xz2 + 2y ) at (2,0, – x COS

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Q: The region is bounded by the graphs of the equations y sin x, y = 0, x=0, and x-A. For the…

A: See this solution in below

Q: 4 - Determine the domain of the function f(1, y) = In(z² + 2y + 1) + arcsin v1- I a)D= {(1, y)|…

A: This question is related to relation and function, we will find the domain of the given function.

Q: (c) Evaluate the line integral 2.xycdx + (x-y)dy where C is from (1,3) to (0,0) along the parabola…

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Q: How would I go about solving ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2…

A: We will find out the limits first.

Q: Let F(x, y, z) = (sin(xy), cos(xy), sin(æyz)). What is the divergence of F at the point (2, –2, 27)?…

A: Given F→=sinxy, cosxy, sinxyz and a point 2,-2,2π

Q: (a) Find that the area of the plane region lying to the right of the parabola x = and to the left of…

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Q: 8. Evaluate the line integral fx'dx + xe 'dy where C is the closed path along the triangle in the…

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Q: Prove that the integral: √ [2xyz² dx + (x²z² + z cos yz)dy + (2x²yz + y cos yz)dz ] Is independent…

A: The given integral is ∫C2xyz2dx+x2z2+zcos yzdy+2x2yz+y cos yzdz. The objective is to prove that the…

Q: The region in the first octant bounded by the coordinate planes, the plane y + z = 2, and the…

A: