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- 30. If E 200 cosh 2x sin 2y a,+ 200 sinh 2x cos 2y a, V/m, find the equation of the di- rection line passing through the point P(1,0,0) and sketch it in the z-0 plane for 0 < x < 5 and 0 < y < /4.Determine the points on the surface y2 + z2 − x = 8 that are closest to the origin. Solve problem using lagrange9.3.16. Compute the surface area of the surface obtained by revolving the given curve about the indicated axis. (a) about the x-axis (b) about x = 4 please answer both a and b 1 to t to 2 x=4t, y=sqrt(t^2) but if you can only do one please do b
- The exact solution of the 2q(z - px - qy) = 1 + q^2 equation and by using this solution,Find the integral surface through the curve y: 2x = y^2 + z^2, y + 1 = 0Consider the surface x^4+ 3xz + z^2+ cos( πxy ) = -2 and the point P0 ( -1, 1, 2) on that surface. Find an equation of (a) the tangent plane at P0 (b) the normal line to the surface at P0Find a generating curve and the axis of revolution for the surface x2 + 3y2 + z2 = 9.
- given the surface revolution x^2+z^2-5y=0 find the equation of its generating curve in the yz-plane rotating through the y-axisFind an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y), (9, 1, 0)Find an equation of the tangent plane to the given surface at the specified point. z= e(x^2)-y2, (1,-1,1)