RELAZIONI E FUNZIONI 191 192 193 194 195 _ _______ lim ( x x + 105 ) x + [0] 196 [ 2] 197 _1_ 198 __________ lim ( x2 4x + 3 x) x + ______ lim x( x2 + 1 x) x + _______ lim ( x(x + 2) x) x + ___________ lim ( x2 7x + 12 x) x + [2] [1] ______ lim ( x2 + 1 x) x + [0] ______ lim ( x2 1 + x) [0] 1 _____ _ lim ___________ x + 1 x [+ ] x x + _____ x + 1 1 199 lim __________ 2 x 0 x [ ] _7_ [ 2 ] sen x 1 cosx Utilizzando i limiti fondamentali (lim _____ = 1 ; lim________ = 0) calcola i seguenti limiti. x 0 x 0 x x esercizio svolto 1 senx lim ________2 x __ x __ 2( 2) 0 Il limite è una forma indeterminata del tipo __; eseguiamo un cambio di variabile ponendo: 0 _ _ _ _ da cui x = z + z=x 2 2 Il limite si riscrive in questo modo: 1 sen(z + __) (1 cosz) _________ (1 + cosz) 1 cosz 1 cos2z 2 lim _____________ = lim _______ = lim _________ = lim __________ = 2 2 2 2 z 0 z 0 z 0 (1 + cosz) z 0 z (1 + cosz) z z z senz 2 1 1 = lim (____) _______ = __ z 0 z 1 + cosz 2 sen3x 200 lim _____ x 0 x tanx 3x 201 lim ____ x 0 senx _ 202 lim ____ x 0 x sen2x x 203 lim _____ x 0 1 cosx x senx sen 205 lim __________ x x 204 lim ________ 3 x 0 [3] _1_ [3] [0] [0] [ ] [ 1] 206 lim __________ senx sen x x [cos ] cosx cos x x [ sen ] 207 lim __________ senx2 x 0 sen x tanx 209 lim _____ x 0 sen3x 208 lim _____ 2 196 x 2sen __ 2 210 lim ______ x 0 x [1] sen2x tanx 211 lim _____ x 0 [0] x2 1 cos2x _1_ 212 lim _________ x 0 [2] sen2x tanx ____ 1 cosx 214 lim _________ x 0 x2 cos2x cosx 215 lim ___________ x 0 x2 cosx senx 216 lim __________ cos2x x __ 213 lim _____ x 0 4 x2 1 cos3x cosx 218 lim ______ _1_ 219 lim (1 x)tan ___ [3] x 1 _3_ [ 2 ] __ 2 ___ [ 2 ] [9] [1] x __ 2 _1_ [4] _2_ 217 lim _________ x 0 [2] _1_ [2] 2x x 2 2 __ [ ]