# Hwk1 - -~ j is-5 Find the directional derivative of f x,y at-1 1 in the direction of-~ i-2 ~ j Q-3 The plane y =-1 intersects the elliptic

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Due date: June 19, 2009, Friday NAME:. .................................................... STUDENT NO:. .................................................... SECTION NUMBER : ..................................................... Math 116 Calculus – Homework # 1 Remark: Solve all the problems. One of the problems, randomly chosen, will be graded. Q-1) Can the function f ( x,y ) = sin x sin 3 y 1 - cos( x 2 + y 2 ) be deﬁned at the origin in such a way that it becomes continuous there? If so, how? Q-2) Directional derivative of a function f ( x,y ) at the point ( - 1 , 1) in the direction ~ i + ~ j is 5, and in the direction ~ i
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Unformatted text preview: -~ j is-5. Find the directional derivative of f ( x,y ) at (-1 , 1) in the direction of-~ i-2 ~ j . Q-3) The plane y =-1 intersects the elliptic paraboloid 2 x 2 + y 2-z = 0 in a parabola. Write parametric equations for the tangent line to this parabola at the point (2 ,-1 , 9). Q-4) Let f ( x,y ) = ( 2 xy ( x 2-y 2 ) x 2 + y 2 , ( x,y ) 6 = (0 , 0) , ( x,y ) = (0 , 0) . Calculate and compare f xy (0 , 0) and f yx (0 , 0). Q-5) Find ∂ 3 ∂t 2 ∂s f ( s 2-cos 2 3 t,e s 2 + 5 t 2 ) in terms of the partial derivatives of f ....
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## This note was uploaded on 10/29/2010 for the course MATH 116 taught by Professor Ahmetguloglu during the Spring '10 term at Bilkent University.

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