Resolution for Quiz 2 - Calculus and Analytic Geometry IV | MATH 2443, Quizzes of Analytical Geometry and Calculus

Download Resolution for Quiz 2 - Calculus and Analytic Geometry IV | MATH 2443 and more Quizzes Analytical Geometry and Calculus in PDF only on Docsity! Quiz 2 Name: k ey 1. For the function f(z, y) = x(e¥ + siny) at the point P(2, 0): a. Find the directional derivative in the direction of the vector v = (3, —4). ; @ }s) Coal Hy S- L edesmy | niles cory) >|, =n 3X4, C7 qo so — © s 2 P- vU.- ~4> 3-H Ut te im diechon of ¥ vas us igi a - Cz, = 7. Da t= Vly = CLarr<s, 32 a [g-## = “(2) b. Find the maximum rate of change of f at P, and the direction in which it occurs. \s) The MAX uy cate 4 Change is in Ne dt feck ox 6 Vel, = =<U4> , awl if eguals [96 (I= vr Sr @ © w 2. Find the equation of the tangent plane to the surface x? + 2ry — y? + 2? = 7 at the \5 point (1, —1, 3). J Lek $lug,t)> x *+2xy -Y 2527 The suche 0 a bayel Surtare fe bf 40 cA yorwel fo % |, =<dee2y, 2x-2y, 221, = <0, 4,6>. © ry teat plane as yormul % <0, 4,6 > quad pats Dru PF (L~Y 3), 30 bas 2g olin O (x-ch + 4lyt) 602-3) 20 @® | ) 3. Find the critical point of the function f(z,y) = x? + ay + 3a + 2y +5. (You do not need to say what kind of critical point it is.) Ak ths crificel pocat, b= gts AOS KY £) Satisfy fPnsy +3= QO. . Sob x22 cearel! Ke 2 70 @ Y= [The Crit cof powwrt AA (~2,1) ©