(b) Find the equation of
the tangent line to the curve
8x^2y^3-5x^2+7y^3=10(x-3y)
, at the point (2,-2).
(c) Given
T''=6x^2y^3-cosx+5y^2-siny+10x^2-e^-3x
; determine:
T'=∫(T'')∂x
T'=∫(T'')∂y
(d) Solve the equation cosecxcosydy-10xdx=0 ,
separably.
Find the equation of the plane tangent to the function f(x, y) =
(x^2)(y^2) cos(xy) at x = y = π / √ 2 . Using this linearization to
approximate f, how good is the approximation L(x, y) ≈ f(x, y) at x
= y = π / √ 2 ? At x = y = 0? At (x, y) = (π, π)?
2.
(a) Find an equation of the tangent plane to the surface
x4 +y4 +z4 = 18 at (2, 1, 1). Find a
derivative in direction (2,2,1) at point (2,1,1). (b) Use Lagrange
multipliers to find the minimum and maximum values of f(x,y,z) = 8x
+ y + z on the surface x4 + y4 + z4 = 18.
10) Find the equation of the line tangent to 8x^2 + 18y^3 = 152
at x = 1.
11) Find dy/dx where x and y are related by the equation xsin(y)
− ycos(x) = 0.005.