1º Bachillera to - Matemáticas - Unidad 1 1 – De rivadas y r epresentación gráfica d) ( ) ≡ x f + = 2 π x tg y 1º - Dib!ar la periódica tgx y = "º - Despla#ar la anterior 2 π a la i#$ierda = x -%&" -'%&( -%& -%&( * %&( %& '%&( %&" = + ≡ 2 π x tg y -∞+ *,1 1 ",1 +∞- -",1 -1 -*,1 - ∞+ ág."(" – 72 a) = x -% -/%&( -'%& -0%&( -%&" -'%&( -%& -%&( * %&( %& '%&( %&" 0%&( '%& /%&( % = + ≡ 2 senx y " 1," 1,"2 1,*( 1 1,*( 1,"2 1," " ",'( ",/1 ",2" ' ",2" ",/1 ",'( " b) = x -%&" -'%&( -%& - %&( * %&( %& '%&( %&" 0% &( '% & /%&( % 2%&( 0%& 1 1%&( = − ≡ 2 senx y -' -",2" -",/1 -",'( -" -1," -1,"2 -1,*( -1 -1,*( -1,"2 -1," -" -",'( -",/1 -",2" c) = x -%&" --'%&( -%& -%&( * %&( %& '%&( %& " 0%& ( '%& /%&( % 2%&( 0%& 11%&( ( ) = + ≡ 2 x sen y *," *,/' 1,2 1 *,21 *,( *,'0 -*,* -*," -*,/' -*,2 -1 -*,21 -*,( -*,'0 *,* d) = x -%&" -'%&( -%& -%&( * %&( %& '%&( %&" 0%&( '%& /%&( % 2%&( 0%& ( ) = − ≡ 2 x sen y *," *,* -*,'0 -*,( -*,21 -1 -*,2 -*,/' -*," -*.* *,'0 *,( *,21 1 *,2 e) = x -%&" -'%&( -% & -%&( * %&( %& '%& ( %&" 0%&( '% & /%&( % 2%&( 0%& 11%&( '%&" = − ≡ senx y 1 *,2" *,/1 *,'( * -*,'( -*,/1 -*,2" -1 -*,2" -*,/1 -*,'( * *,'( *,/1 *,2" 1 f) = x -%&" -'%&( -%& -%&( * %&( %& '%&( %&" 0%&( '%& /%&( % 2%&( 0%& 11%&( ( ) = − ≡ x sen y 1 *,2" *,/1 *,'( * -*,'( -*,/1 -*,2" -1 -*,2" -*,/1 -*,'( * *,'( *,/1 *,2" g) = x -%&" -'%&( - %& -%&( * %&( %& '%& ( %&" 0%&( '%& /%&( % 2%&( 0%& 1 1%&( = ≡ senx y 1 *,2" * ,/1 *,'( * *,'( *,/1 *,2" 1 *,2" *,/1 *,'( * *,'( *,/1 *,2" h) = x -%&" -'%&( -%& -%&( * %&( %& '%&( % &" 0%&( '%& /%&( % 2%&( 0%& 11%&( = ≡ x sen y 1 *,2" *,/1 *,'( * -*,'( -*,/1 -*,2" -1 -*,2" -*,/1 -*,'( * *,'( *,/1 *,2" i) = x -%&" -'%&( -%& -%&( * %&( %& '%&( % &" 0%&( '%& /%&( % 2%&( 0%& 1 1%&( = ≡ senx y 2 -" -1,( -1," -*,/ * *,/ 1," 1,( " 1,( 1," *,/ * -*,/ -1," -1,( !) = x * %&1 %&( '%&1 %& 0%&1 '%&( /%&1 %&" 2%&1 0%&( 11%&1 '%& ( ) = ≡ x sen y 2 * *,'( *,/1 *,2" 1 *,2" *,/1 *,'( * -*,'( -*,/1 -*,2" -1 ág."(" – 73 1 2 2 2 − − = x x L y ( ) ( ) 1 2 2 4 2 2 ' 2 2 − − + − = x x x x y a) ( ) ( ) { } 0 1 2 2 // 2 > − − ∈ = x x R x D ⇒ +∞ • ∪ • − 2 2 1 2 3orte 456 → = 0 y ( ) ( ) → = − − 1 1 2 2 2 x x 2 1 ± = x 3orte 476 → = 0 x 2 L y = 69 , 0 ≅ ( ) +∞ = → − y x lím 2 1 . −∞ = ± → 2 . x lím ⇒ 8s9ntotas6 2 1 = x 2 ± = x b) 0 ' > y ( ) D x ∈ → ciente SiempreCre y = c) = x -1, -1,' -1," -1,1 -1 -*,/0 -*0* -*,1" -*,' -*,1 * *," *, *,0 = y -,00 -",0 -1,(* -1,* -1,1* -*.00 -*,1' * *,1( *,01 *,2 1,1( ","" + ∞
