Question

lim X3 ws #1 use E-s limit definition to prove #2 Find an equation of the tangent line at (1,1) on the curve y4+xy =X3_x+2.

Answer 1

Let E>O and 023 there is Ix-ales - If (x) -11 LE lim x a f (x ) L. Take E- S >o There is so (stele Ix-31 Lo =) se-e XE [: 14-3/<8 » -8ca- 34s X-3 3x => 3-8 < X <3+ → X< 3+] be-3 | 3121 ] co < CScanned with CamScanner 3(3+8)

= E. ㅅ 33 +8) For E>o I so 1x -31<8 => 1. 3기 우 e 3 . Lim 93 3 CScanned with CamScanner

xy + y + = x² -x + 2 We need to curve find tangent (1,1) to at the given point First find slope of -curve dy - di levo So, differentiate both side Wort. x 1 xy + y^) - 4(x23 -x +2 ) da dx y + x dy de + 4y3 day 3x² il dx dy die 3 x² y - ) 1+ 4 y3 de la loi vil- 1,1) Scanned with CamScanner

Finally equation of equation of tangent line -. - m(-) (y-1]. 눙 (1) 5 y - L 4 L. 5 > - * + 4 5 에서 - 9 + 1 -1 쇼 5 -9 +4 5 5 M - 5Y+4 0 CScanned with CamScanner