5. Evaluate f (x²zdx – yx²dy + 3dz) where C is the boundary of the triangle with vertices (0,0, 0), (1, 1, 0) and ( 1, 1, 1).

Q: Evaluate the line integral S 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). So…

A:

Q: Suppose f(x, y, z) = In(7x + 9y+7z). Find an equation for the level surface of f that passes through…

A: Given Data: The level of the curve for fx,y,z=In 7x2+9y+7z2 is of the form,…

Q: Sketch in the two level curves of: f (x, y) = y+ x² = k _for k = 1, 2.

A: Solution is written in below steps.

Q: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x +…

A: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x + y…

Q: 20. Show that a²F(x, y) -dx dy дх ду over the rectangle xo < x < x1, Yo < y < y1, is F(x, у) — F(x0.…

A:

Q: Calculate the are bounded by the curves: C. y = e2x and x - 2y + 5 = 0

A: Introduction: The formula of the area between the curves y=f(x) and y=g(x) is given by,…

Q: A funchion is defined by +the formua a f(x)=Ź ) which of the follauing is the %3D value of

A:

Q: Set up the line integral ∫c x2z ds, where c is the line segment from (1, 6, -1) to (- 4, 1, 5). (No…

A:

Q: Use LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2,…

A: Given surface z2=x2+y2 and the point (4,2,0). The objective is to find the points on the surface…

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: 5. Conclude on the limit of f(x, y) = +v4 xy2 as (x, y) → (0,0) along paths y = mx and x = y?

A:

Q: Evaluate F- dr where F(, y, z) = (1.5yz cos(ryz), 1.5xzcos(ryz), 1.5xy cos(ryz)) and C (*) is the…

A: We need to evaluate the line integral between the two points.

Q: Show that the minimum distance from the origin to a point on theplane ax + by + cz = d is

A: Given: ax+by+cz=d we know that minimum distance p of a point x1,y1,z1 from given equation of plane…

Q: If C is the line segment which begins at (-2, 1) and ends at (2, 4), evaluate the line integral: et…

A:

Q: Show that if a two-parameter family of surfaces f(x, y, z, 1, µ) = 0 has an envelope, then the…

A:

Q: Find the maximum value of f(x, y) = 11zy(9 – 99x – 9y) over the triangle with vertices (0, 0). (†,0)…

A: Given: The triangle vertices are (0,0),(111,0) and (0,1) f(x,y)=11xy(9-99x-9y)…

Q: Consider the inmplicitly defined curve xy +3x2 4. %3D O Verify that the point (1, 1) is on the…

A: Consider, the implicitely defined curve                          xy2+3x2=4 We have to verify the…

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

A:

Q: Show that if y is the boundary

A: To prove that if γ is the boundary of the trianglee with vertices at z=0, z=3i,and z=-4 oriented in…

Q: Find the maximum and minimum values of f(x, y) = x² + 2y² on the quarter circle x² + y² ≤ 4 with r,…

A:

Q: 1. A such that the difference in distances between (x, y) and two fixed points (called is the set of…

A: A___ is the set of points (x, y) in a plane such that the difference in distances between (x, y) and…

Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: Evaluate f(x,y,z) dS 2. 3DX²+4y+z on the surface S {(x,y,z):05xS2, y= 3, 1Sz5 4)

A:

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: Evaluate the line integral Sc (2x² − 3y) dx + xy dy, where the curve/path C is the line 3 y = 2/2 x…

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Q: Evaluate f 3z2dz over C, where C is the upper half circle |z – connects points O and 1+i. -글히 %3D플…

A:

Q: 10) Use Green's Theorem to eualuate S+10ny +y?)dx + l6xy+ 5a²) dy Toxy+ sa?) dy where C is the…

A:

Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

A:

Q: Find the are bounded by the curve y=x²-4, the lines y=0 and x=4.

A:

Q: Let C be the line segment connecting 0 to ni. Then f. 1-e2z dz =

A: we have to find integration

Q: The area bounded by the curve y = 4r and the lines z = 2 and I=8 above the I- aris is O 240.00…

A:

Q: 2. Calculate (y+ z)dx+(x+z)dy + (x+ y)dz , where C consists of line segments from (0,0,0) to (3,2,4)…

A:

Q: 4) Suppose that the level curves of a function z = f (x, y) consists of straight lines. Must the…

A: Given that level curve of a function z=f(x,y) consists of straight lines.

Q: Use LaGrange multipliers to find the minimum distance between the origin and the plane x+2y+3z=28.

A:

Q: Find the surfaces on which the function u = 2 (x2 + y²)/z is constar

A: Since u is a constant so, x2+y2z=4a , where a is an arbitrary constant.

Q: 4. Let f(x, y, z) = e² + zy² and let C be a straight line segment connecting the points (4,2,1) and…

A:

Q: can u help me with pullbacks and integration plz

A: Given that the integral,

Q: If C is the line segment from (1, 4, 2) to (3, 2, 1), evaluate the line integral y+ 2) ds.

A: Express the line segment in its parametric form and then use the formula below to evaluate the line…

Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y²-x²y = 0 2y +…

A:

Q: Compute (x² + 2y + 3z +1) ds where Cis the line segment from (0, 2, 3) to (2, 5, 7).

A:

Q: Evaluate the line integral 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). Sc…

A:

Q: Show that f(-ydx + xdy) where C is the line segment joining (x, y) and (x₂, y2).

A:

Q: Find the families of characteristics of the PDE (1-x²)w„ - u,, = 0 in the elliptic and hyperbolic…

A: Pde

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: 5) Consider the surfaces S1 : ryz = 10 and S2 : z =r² + y and the %3D point Po = (1,2,5).

A:

Q: Determine the location of a point (x, y, z) that satisfies the condition(s). xy &gt; 0, z = −3

A: Here Our Aim is to determine the location of a point (x,y,z) that satisfiesthe condition(s):→…

Q: Find the points on the cone z2 = x² + y2 that are closest to the point (8, 2, 0).

A: we have given the equation of cone z2=x2+y2 and the point (8,2,0)to…

Q: 5. Show that the following orthogonal families of curves: are x² + y² : = ax, x² + y? = by

A:

Q: Evaluate | xyzdx + In(xy)dy + xzdz over the straight line segment from (2, 1, 1) to (–1,1, –2)

A: We need to evaluate integral∫Cxyzdx+lnxydy+xzdz over the line segment from 2,1,1 to -1,1,-2.

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.