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find unit tangent
r(t)=(4-2t)i+(2t-3)j+(8+t^2)k
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- Find the two-unit vectors that are parallel to the tangent line to the curve y =x2sin(x) at the point (π/2, π2/4).Find a unit vector tangent to the curve of intersection of -x^2 - 2y^3 = z - 3 and 25/x2 - 4y - 3z^2 = - x + 6 at the point (1,1,0).Find a vector equation for the tangent line to the curve of intersection of the cylinders x2+y2=25 and y2+z2=20 at the point (3, 4, 2).
- Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and is parallel to the tangent line to y = 10 + 4x−x^(2) at x = 3.Find the tangent plane to the equation z=−3x2−y2−4yz=-3x2-y2-4y at the point (4,2,−60)(4,2,-60)Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the point (2,1) is maximum. What is this maximum rate of change?
- Find the equation of the tangent plane to z=6x2+2y2 at the point (1,5)Find the slope of the tangent line to the curve of intersection of the graph of z = 2x2 + 3xy + 2y2 + 3 and the plane x = 1 at the point (1, 0, 5).Find the equations of the tangent plane and the normal line at point (1,1,-2) to surface z^2 = x^2-y^2+4