Question

M ULIJJJ040_1Wurses/5_202020_22458_MATH_01230/test2%2011 6. (10 pts.) Evaluate the limit if it exists or show the limit does not exist: (a) lim(=,y)=(2,1) 7°+27° In(4 - ry) (b) lim(.)=(0,0) 7. (12 pts.) If : = 2 cos r + ex-3y, (a) find is, zy, že tay, and zwy (or if you prefer to and ). (b) Evaluate all these derivatives at the origin.

Answer 1

solution: _ Given that 6) a lime (14) > (21) e y in 14-44) z e87261 in (4-2-1) ze4+? In (2) се вint) prehry muy extrast in (sas) z e®me) yamn Choose a path lim Gemn)(0,0) Noma x²tmine lim sam 270 aritme) - lim m ano Time ndo Am2 Itm? 2 m , which depends mm. For different values of m, we get ditterent limit (ie not unique ) so the limit does not enist.

SARILIN LYS LLLLL PRO solution. Given that o @ Zn2cosnt 233-37 13232- 3 (2com +228 33) Zn -- 2sim + e*-372n Zn = -2 sinn + ane 2-3y I Zxn = 35 (32) 22 m (-2simtine #3y) Zyon 2 -2 event 3.18x37 .. +20.02239 24 Zur 2-20usn +202=32 4200 234 Zara -20osh &/2+42²) exaby 2y = 28 (2) I zy = 3/4 (2con ote2=3y) 2y 20+ e$37.-3) | 2y = -3 e 2-3y Zyy - og C2y) (-342357) 2-32*39(-3) = 928538 1. Zgy a gemasy] remember

2xy = a +) 29 (-- Sibn taxe »37) 20+ 2xer-> (3) – 6 хезу П: 2х1 = — 6x е 2 |