Find I, for the curve x = tcost, y = tsint and z = t² if ♪ (density) is proportional to √(1+52) from t=0 to t=1. Iz = Should have a factor of 'K' in it, where K is some proportionality constant.

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

A:

Q: Find the equation for the tangent plane and the normal line at the point Po(1,2,1) on the surface…

A: The given problem is to find the equation of tangent plane to the surface and equation of normal…

Q: Find the plane tangent to the function z = √y at the point (5, 16). L(x, y) =

A:

Q: Sketch the level curves for f(x, y) typical points. Write an equation for the tangent line of the…

A: If , then the independent variable x is called the input of the function and the dependent variable…

Q: Find the equation of the tangent plane to z = x² + 5y³ at (2, 1, 9).

A:

Q: Find the equation of the tangent plane to z = e* + y + y° +1 at the point (0, 4, 70).

A:

Q: II. Consider the function g defined by g(x, y) 3 = cos (Tx /y) + х — у Do as indicated. 1. Determine…

A:

Q: Find an equation of the tangent plane at the given point. f (x, y) = x/√y,  (4, 4)

A: Given : The function is f ( x, y) = xy and point ( 4, 4 ).

Q: Find the equation of the tangent plane to f(x, y) = x² - 2xy + 5y2 having slope 2 in the positive x…

A:

Q: Find the equation of the tangent plane to z = e² + y + y² +8 at the point (0, 4, 269). Z= 0

A:

Q: Determine the intersection point of the lines tangent to the curve r (t) = (senπt, 2senπt, cosπt) at…

A: The given curve is rt=sinπt,2sinπt,cosπt. Differentiating it with respect to t:…

Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

A:

Q: Find an equation of the plane tangent to the following surface at the given points. z=ln(1+xy)​;…

A:

Q: For the function f(x, y) = 2x² – 3xy + 8y² + 2x – 4y + 4, find a tangent vector to the level curve…

A: