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

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: Find the length of the arc of the parabola  x^2 = 4y from x = -2  to x = 2.

A: I am attaching image so that you understand each and every step.

Q: Use Green's theorem to calculate §. -y² dx + xy dy where C is the vertex triangle (1,3), (4,0) and…

A: Consider the given integral. I=∮c-y2dx+xydy The green theorem is defined as, ∮cPdx+Qdy=∬R∂Q∂y−∂P∂x…

Q: Find the distance from the origin to the plane 2 = z - x.

A: Given point is (0,0,0) Given plane is 2=z-x or x-z+2=0

Q: 7. Derive the orthogonal trajectories of the family of hyperbolas xy = c. %3D

A: The solution are next step

Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: Find the arclength of y = 2x3/2 on the interval x is greater than or equal to 1 and less than or…

A: Equation of given curve is y=2x32 Differentiate with respect to x. dydx=232x32-1=3x

Q: Find the points on the cone z2 = x² + y² that are closest to the point (1,-1,0) %3D

A: Given that, z2=x2+y2 and the point is (1, -1,0). Form the equation of distance as follows.…

Q: Find the equation of the tangent plane to the surface y = 2x2 - z2 at the point (0, –1, –1) %3D | |

A:

Q: 2. Find the equation of the plane tangent to the elliptic paraboloid z = point (1, 1,3). 2.a2 +y, at…

A: To find out the equation of the plane tangent to the elliptic paraboloid.

Q: Find three different parametrizations of the graph of y = x3.

A:

Q: ) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A:

Q: Find the tangent plane to the equation 3y cos(4x – 2y) at the point (2,4,12) Z =

A: Z=3ycos(4x-2y)  Point= (2,4,12)

Q: 8. Determine the equation of the plane tangent to z point (x, у, z) 3 (-2, 1, 4). x*y3 at the =

A:

Q: 4 Find a parametrization for the line segment with endpoints (-1,3) and (3,-2).

A: 4) To find the parametric equation of line segment with endpoints (-1,3) & (3,-2)

Q: Find the tangent plane to the equation 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

A:

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: Q1/ plot x2-y2=z (Elliptic paraboloid) in 3D.

A: Topic:- plot in 3-D

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 = 0 that are closest to the origin. please…

A:

Q: Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci on…

A:

Q: function holomorphic in 2 except p in an open neighborhood of w, the

A: To prove, ∫Tf(z)dz=0

Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch the…

A:

Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: Find the point P nearest to Q = (−1, 3, −1) on the planex − 4z = 2

A:

Q: Find the appropriate parametrization for the given piecewise smooth-curvein R^2, with the implied…

A: Here, a semi-circle is of radius 3.

Q: Find the distance between the point (0, 0, 0) and the plane 2x + 3y + z = 12.

A:

Q: Find the arclength of y = 2x /2 on 1 < ¤ < 3 2x3/2 uostion

A: given that y=2x3/2. we need to find the arc length in the interval [1,3] the arc length formulae is…

Q: 5. plot x?-y?=z (Elliptic paraboloid) in 3D.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0),…

A:

Q: Sketch the surfaces PARABOLOIDS AND CONES x = 4 - 4y2 - z2

A: The given equation is x = 4 - 4y2 - z2

Q: Compute ,f for f(2) +6 + 6i, positively oriented. sin(32) and path 2 that is the boundary of the…

A: Let's see the method of integration. We use residue method to solve this integral.

Q: Find the arclength of y = 3x2 -5 on x is greater than or equal to 0 and less than or equal to 2

A:

Q: Find the tangent plane to the equation z 2y cos(3r - 6y) at the point (6,3,6) %3D

A:

Q: Find the parametric equations of the tangent line to the curve of intersection of the surfaces x² -…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin. please…

A: The parametric equation of hyperbolic cylinderx2-z2-1=0 is , x=cos hθ                          y=y…

Q: 4. Find an equation for the tangent plane to the surface z = 3x + 5y + arctan in the point (0, 1,…

A:

Q: parametrically

A:

Q: Find the tangent plane to the elliptic paraboloid z = x² – 2y at the point (1,1,1). - O A. z = 2x –…

A: Given that: z=x2-2y2      and point is:   (1, 1, 1)

Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

A:

Q: 1. Tangent to the parabola z = x + 3y?, x = 1, at point (1,2, 13

A:

Q: Find the area of on of the triangle that can drawn between the planes Зх — бу- 2г 15 and 2x + y - 2z…

A:

Q: Does the the paraboloid z = 1 – 2x² - - y² have a tangent plane at some – x + y + z = 1?

A: Introduction: Let P0=(x0,y0) is a point in the domain of f, and S is a surface defined by a…

Q: Find the gardientoff at the indicatedpoint. %3D

A: Given,

Q: Consider the equation хд,и — удуи — -и with the initial condition: u(x,y) : = 2 on the circle {(x,y)…

A: Given the equation as x∂xu-y∂yu=-u                  (1) write down the subsidiary equation of (1)…

Q: Find the arclength of y = 4x2 - 4 where x is greater than or equal to 0 and less than or equal to 4

A: Concept Used: The arc length of the function is the length of the curve y=fx on the interval a,b is…

Q: The tangent plane to the elliptic paraboloid z = -2x - 7y? at the point (-3, -4) is

A: Consider the provided question, The equation of the tangent plane to the elliptic paraboloid at the…

Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

Q: 10. Find a tangent plane to z² – x² +y² = 1 at (7, –5, 5).

A: To find a tangent plane to the given curve at the point (7,-5,5)

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.