By means of Stokes' Theorem, find | F. dŘ 3.x, on the ellipse x² + y? = 1, z = F = xỉ+ (x + y)3+ (x + y + z). The ellipse is traced counterclockwise if we look back at it from the direction of the positive z-axis.

Q: 6. The ellipsoid + y2 + z2 = 4 and the plane y = 1 intersect to form an ellipse. Find slope of the…

A: Given:

Q: where does this concave up and down?

A: A graph is concave up if f''x>0 and concave down if f''x<0. When f''x>0, it means…

Q: d. P = 4x1 – 2x2, Q = 2x1 + 6x2; D is the interior of the ellipse: x1 = 2 cos 0, x2 = = sin 0, 0 E…

A:

Q: Show that the ellipse x*/a? + y*/b? = 1 and the hyperbola x/A? – y/B² = 1 are orthogonal…

A:

Q: Describe the surface whose equation is given by x² + y² + z² + 6y - 2z = 0.

A:

Q: Consider the paraboloid given by the equation: z = x^2 + y^2 Find the equation of the tangent…

A: at point (1, 2, 5)at point (1, 2, 5)

Q: Find the trace of the surface 4x^2 − y^2 +6z^2 = 2 in the yz-plane and identify the conic section.

A: Given 4x2-y2+6z2=2

Q: The surface of a paraboloid results from rotating a parabola about its axis. the parametric form is…

A: The objective of the question is to understand how the shape of a paraboloid changes when the…

Q: ) Find the derivetine of the fnchiog h(x) = I sinhex-7x 4

A: h(x)=74sinh(2x)-7x2Differentiate w.r.t…