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

Q: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and

A:

Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

Q: Find a parametrization of the vertical line passing through the point (9, 5, 0) using t = z as a…

A:

Q: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

Q: Find a parametrization of the right branch (x > 0) of the hyperbola(x/a)2−*(y/b)2= 1 using cosh…

A: Given that. xa2-yb2=1     ...(1) Need to evaluate parametrize form of (1).

Q: Find the equation for the tangent plane to the surface z=ln(4x2 +3y2 +1) at the point (0,0,0)

A:

Q: (4) The equation of the tangent plane to the surface In = z²(x – 2y) + 3z +3 at (4, 2, –1) is 2y

A:

Q: Find the equation of the tangent plane to th surface 3x? + 5y? + 4z2 = 24 at the point (1, –1,2). 1.…

A:

Q: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

A:

Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

A:

Q: Find all points on the ellipse x2 - xy + y2 = 1 at which the tangent line is horizontal.

A: The given equation of ellipse is,

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 parametric equations for the tangent line to the curve of intersection of the paraboloid   z =…

A: The given curve is the intersection of paraboloid z = x2+y2 and ellipsoid 3x2+2y2+6z2 = 29.

Q: Find the equation of the tangent plane to the surface y = 2x2 – z2 at the point (0, –1, –1) y+ 4z =…

A: We have to find

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

A:

Q: set up intergral for the length an of the Curve 3T y%3DZ0* sin cx), 04XE

A:

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: Determine the parametric equation for a line that is tangent (intersection) of the two fields below:…

A: We have to find out parametric equation for a line that is tangent (intersection)of the two fields…

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 <=t<= 2pai closest to the point (3/4,…

A:

Q: Find the derivative dydx of the hyperbolic spiral r=aθ.

A:

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

A:

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x = 74…

A: given curves x2+z2=74 , y2+z2=74 , point 5,-5,7  to find parametric equations for the tangent line…

Q: A-Estimate J, 2e-3* dx using trapezoidal rule with four subinterval round your answer to one decimal…

A: Given is the integral  ∫-11 2e-3xdx The aim is evaluate the integral using trapezoidal rule.

Q: 3. Find the radius and center of curvature of the parabola y=x²-4x+4 at any point (x,y)on the curve.

A:

Q: Find the least squares quadratic & bj xj which best fits curve Y = sin(x)

A:

Q: dy Use the method of isoclines to draw several solution curves for the equation dr

A: First integrate the function using variable separation method and find y as function of x  Then draw…

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

Q: Show that the tangent line at a point P = (x0, y0) on the hyperbola(x/a)2−(y/b)2= 1 has equation Ax…

A: Given equation of hyperbola  x2a2-y2b2=1 and given point is P=xo,yo. Since hyperbola is passing…

Q: A point moves along the intersection of the elliptic paraboloid z = 9x + 7y and the planex = 1. At…

A:

Q: 4) Find the families of lines of curvature of the surface : =+ y² .

A: Given: z=x2+y2

Q: How do I find the bounds in which I integrate a curve that is rotated about an axis?

A: To find the bounds, it is necessary to check whether we have to find the surface area or volume. In…

Q: (iii) dz< 22 + 2 where here y parametrises the straight line segment from 0 to 1- i.

A:

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: Differentiate parametrically to find x=3t², y=6t dy dx in terms of t:

A:

Q: 4. Find the equation of the tangent plane to the surface ey + In(xz) – evz = 0 at the point (1,0,…

A: Given:

Q: ind an equation for the tangent plane of z = –2x²y – 3x² + y at the point (1, –1, –2).

A:

Q: Q1) Find equation of line normal to plane 3x + 2y - z = 5 and pass through Origin point.

A:

Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

A:

Q: 2dy -2y 2. zt at

A: Solved below

Q: Calculate the curve integral ∫c ( 3x2 - 3yz + 2xz )dx + ( 3y2 - 3xz +z2 )dy + ( 3z2 - 3xy + x2 +2yz…

A: Using green's theorem to find the line integral.

Q: Find the length of the curve y Inx at (2<x< 4)?

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: #5. Evaluate the line integral (xydx +2x dy), where C is the arc of the parabola with equation y=…

A:

Q: Find the arclength on y = 4x3/2 from x is greater than or equal to 1 and less than or equal to 3

A: given: the function is y=4x32. we have to find the arc length on y=4x32 from x is greater than or…

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: Find a point on the ellipsoid 3x2 + y2 + 3z2 = 1 where the tangent line is parallel to the plane…

A: Given: The equation of ellipsoid is 3x2+y2+3z2=1 and the equation of the plane is -12x+2y+6z=0.…