Question

(1 point) Estimate f(-3.01,-1.97) given that f(-3,-2) = 5, fx(-3,-2) = -2 and fy(-3, -2) = 3. f(-3.01,-1.97) ~

Answer 1

as we want to estimate f(-3.01, -1.97) $143,-3) = 5, fre (-3,-2)=-2, given that fy (-3,-2) = 3 we know f(x,y) a fl26,%) + fx (2o, %o) (x-%0) + fy (86,00) (Y-Y) Mere Xo = -3, y=-2 Now +(-3.01,-1.97) f(-3,-2) + fx (-3,-2) (-3001-(-3)). ..t fy (-3,-2) (-1.97 -(-2)) fi (5+ (-2)(-.01) + (3) (0.03) f(-3.01, -1.90) 3 [5.11] [a. Given the function z=xfo and point (-5, 40) - we want to calcalute the linearization .: f(x, y) = 2 = x 57 we know 2(x,y) = f(-5, 49) + fx (-5, 40) (x-1-5)) + fy(-5,49) (4-49) Now fx (X,Y)= 2 r (25g) = sy 2 (2) = 55 fy (8,y) = 2 ( x 5g) = x 2 (52) = 2 2 5% fxl-5,49) = 549=7, fyl-5,48)= -x t = -2 f(-5,49)= (-5) (+) = -35 : 119x) = (-35) + (1) (+5) + (-) (8-45) - L(9,8) = -35 +72 +35 - Ray+ 35 - 13:15) = 112-post

LI @] Given the 2= ex+y+4+6 we want to find Equation of tangrant plane at 1 we know equation of tangent plane at (86,50, 20) z- zo= fxx(62o, 3o) (x-2) + fy (2o, 3o) (9-%) 0 Here f(x,y) = x+y+ya+6, (2o, yo, 20) = (0,3,91) Now folx, y) = a (erty ty9+6)=eto toto=ex fx l 0,3) = e = 1 fy (2,4)=B (+y+91+C) = 0+1+45°+0 = 1tay fy 10, 3) = 144(35° = 109 .. Equation of tangent pane 2-917 () (-0) +(109) (9- 3) - 2-91 = x + 109 y - 327 = z= I + 10gy - 327+81 z=lat logy - 236