ди dt 00 dx2 ди u(0, г) — 0 %3DИо, %3D -h (u (1,1) — ио), һ>0, t>0 and u(x, 0) %3D f(x), 0

Q: Caleulate all first ordeT partial derivatives of the finction y 2nin(r²) ekan '(-y) + + cos2(xz2)

A: We need to calculate all first-order partial derivatives of the function w=yz…

Q: 5. (x² + y2 + 1)dx + x(x – 2y)dy = 0,x = 2,y = 3 %3D

A: Solution

Q: 8. The region of integration D is bounded by the lines y = x,x + y ==,y = 0. Show that 1 | sin(x +…

A:

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) Jazy…

A:

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

A:

Q: The possible error involved in measuring each dimension of a rectangular box is ±0.1 mm. The…

A: Given: The dimensions of the box are x = 50 cm, y = 20 cm and z = 15 cm. The possible error involved…

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

A:

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) | 5x*y…

A: We have to prove that differential form in the integral is exact.

Q: Find the centroid of the solid formed by revolving about ox the area bounded by y^2=2x and the line…

A:

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: 10

A: Given:

Q: Find a center of mass of a thin plate of density 8 = 6 bounded by the lines y=x and x = 0 and the…

A:

Q: 5. Classify the following partial differential equati ons :

A:

Q: Solve by integration: Find the centroid of the region bounded by y=x3+3 and the lines x=0 and y=0.…

A: given functions are                                              y=x3+3x=0y=0…

Q: -Svau Using Integration By Parts, x Arcsec 3x dx = uv- - Svau- Find uv- x² Arcsec 3x dx V9x2 – 1 o 1…

A: Here we have to solve the integration by using integration by parts.

Q: Explain why the function is differentiable at the given point. 4x f(x, y) = y + sin (0, 6) The…

A:

Q: Sketch the region of integration. (Select the correct graph.) "In 3 dy dx In y y y

A:

Q: 8 Evelluate the double integral: + 3x) dydx

A:

Q: 4. The area of the region between the curve y=x* and the line y%3D4 is divided into equal partitions…

A: Given curves are y=x2 and y=4.Also given that y=c divided into equal parts of the area.

Q: Find the volume of the solid generated by revolving the region bounded by 1 about the line x = 3…

A: Given equation y=x2-2x+2 and x=0, x=1, y=1 about the line x=3

Q: A Korean corn dog is a cylindrical piece of hotdog, rice cake, or mozzarella cheese, evenly coated…

A: Given: Calculate how much larger (in cm2) the cross-sectional area of the XXL item C is compared to…

Q: find all second partial derivatives:  f(x,y) = ex + tan (x+y^2) i got fx= ex + sec^2 (x+y^2)…

A: We will solve the following partial derivative.

Q: Evaluate the integral. 1//3 3earctan(y) dy -V3 1 + y2

A:

Q: For some regions, both the washer and shell methods work well for the solid generated by revolving…

A: Given: y=x y=x2 Solve the equation y=x and y=x2 for y. y=y2y2-y=0y(y-1)=0y=0,1 Rewrite the…

Q: The volume of the solid obtained by rotating the region bounded by y=(x^2), y=3x  about the line y=9…

A:

Q: Svain2x dx =uv- fvdu - Svau. x/x In 2x- Vx dx v- Svau- Using Integration By Parts, Find uv- Jv du O…

A: Find your answer below

Q: FIND THE CENTROID OF THE REGION IN THE FIRST QUADRANT BOUNDED BY THE GRAPH OF y=9-x2, THE X-AXIS,…

A: Given region is bounded by the graph of  y=9-x2, The X-axis and Y-axis

Q: Sketch the region R of integration and switch the order of integration. 81-x2 LV²²- -10 O -10 f(x,…

A:

Q: Prove that div curl v = 0 where the components of v have continuous second partial derivatives

A:

Q: volume of solid of as revolution y^2=4x and x^2=4y about the x axis

A:

Q: volume of the solid obtained by rotating the region bounded by y=x^2, y=3x about the line x = 3…

A: In this question, the concept of the volume of revolution about the line is applied. Given,…

Q: Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0, 6) and…

A: Given Line Integral is ∮x4dx+xydy , where C is a triangle with vertices at (0,0), (0,6) and (6,0)…

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

A:

Q: 8. cos x sin y dx +(3xy+sin x cos y) dy and y = \x 4oil C:boundary of the region lying between the…

A: Given that ∫Ccos x sin y dx+(3xy+ sin x cos y)dy ;y=x4, y=x Using Green's theorem ∫CP dx+Q…

Q: Show complete solution (with graph). 1. Determine the centroid of the area bounded by the y − axis,…

A:

Q: Find the area and centroid bounded by y^2=-x, x^2+3y+4x+6=0. Graph

A:

Q: The full solution y is obtained by adding the complementary solution to the particular integral, y =…

A:

Q: A Korean corn dog is a cylindrical piece of hotdog, rice cake, or mozzarella cheese, evenly coated…

A: We will use total derivative to find change  If f is a function of x and y  ∆f=∆x×∂f∂x+∆y×∂f∂y

Q: Solid created from these conditiong limited to 0eyet fiest actant on ly Positive xy-plane

A: y=xx=y2,0≤y≤10≤x≤y2z=1-yy=1-z0≤y≤1-z,0≤z≤1V=∫01∫01-z∫0y2 dx dy dz

Q: Compute the partial derivatives: z = sinh(r²y^) az ||

A: We will find out the required values.

Q: 4. Triple Integration Evaluate the equation below 1 - In y ex+y+z dx dy dz

A: Given: ∫01∫0z∫0ln yex+y+zdxdydz

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: both first partial derivatives. z = exy %3D az %3D ax %3D ay

A: Solve above problem.

Q: Can you conclude anything about ƒ(a, b) if ƒ and its first and second partial derivatives are…

A:

Q: Sudv= 2x)dx can be evaluated using integration by parts of the form v=uv

A:

Q: Find the centroid of the region bounded by the graphs of the equations using any method y = √(1 −…

A: Consider the given equations y=fx=1-x2y=gx=0 First, find the point of intersection of the given…

Q: Solve using integrable combination technique only: (x^2y^3−(6+1)y)dx+(x^3y^2+(9+1)x)dy=0

A: Solve using integrable combination technique only: (x^2y^3−(6+1)y)dx+(x^3y^2+(9+1)x)dy=0

Q: Given function f(x,y) = 1 + xy – x - y. a) using partial differential involving limits to obtain…

A: Critical points of a function f(x, y) is given by,  fx(x,y)=0andfy(x,y)=0 Now if (a, b) is any…

Q: IT Evaluate the proper integration from 0 to 4 of arctan x. Leave your answer in terms of r.

A: