alloproflala

# alloproflala - (d Find the eq of straight line tangent...

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CT2 Math262FALL2011 Name Student ID The assignment submitted is my own work: Sign here ____________ 1. If ( , ) z f x y = , where sin x t s = and cos y t s = , find 2 z s t ∂ ∂ , 2 2 z s and 2 2 z t ; in terms of the partial derivatives of f(x,y) w.r.t. x and y. 2. Use suitable linearization to find approximate values for the given function 2 ( , ) (2.05, 3.92). y x f x y xe at + = - 3. Given 2 ( , ) 1 f x y xy = + (a) Find the gradient of given function at point (2, -2). (b) Find the directional derivative of f(x,y) at (2, -2) in the direction of - i j . (c) Find the eq. of tangnt plane at (2, -2).
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Unformatted text preview: (d) Find the eq. of straight line tangent at (2, -2) , to the level curve of given function passing through that point. 4. Find a vector tangent to curve of intersection of two cylinders 2 2 2 x y + = and 2 2 2 x z + = at point (1, -1, 1). 5. Given 2 2 2 2 1 x y z w + + + = 2 3 4 2 x y z w + + + = , where ( , ) x x y z = and ( , ) w w y z = . Find z x y ∂ ∂ and y w z ∂ ∂ provided that 4 . w x ≠...
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