32)

limx→0

sen4 x2 x

=¿ sen 4(0)2(0)

=¿ (0)(0)→Indeterminado

limx→0

sen 4 x4 x

.4 x

2 x=

limx→0 ( sen4 x

4 x.4 x )

limx→0

2x = (

limx→0

sen4 x

4 x ). limx→0

(4 x )

limx→0

2 x =

(1 ) limx→0

(4 x )

limx→0

2 x = limx→0 ( 4 x

2 x )

= limx→02 = 2 Respuesta

33)

limx→0

sen2x12x =

sen2(0)

12(0) = sen0

0 = 00 →Indeterminado

limx→0

sen2 x2x

.2x

12x

= limx→0 ( sen2 x

2 x.2x)

limx→0

1

2x

= ( limx→ 0

sen2 x

2 x ). limx→ 0

(2 x )

limx→0

1

2 x

= (1 ) lim

x→0(2x )

limx→0

1

2 x =

limx→0 ( 2 x

12x ) = lim

x→0(4 ) = 4 Respuesta

34) limx→0

tan x2 x = tan 0

2(0)=¿ 0

0→indeterminada

limx→0

sen xcos x2x

= limx→0

sen x2 xcos x = lim

x→0

sen xx. x

2 xcos x =

= limx→ 0 ( sen xx . x)limx→0

2xcos x=

limx→ 0 ( sen xx )( lim

x→0x)

( limx→0

2 x)( limx→0

cos x ) =

( limx→0

x)

( limx→0

2 x) =

= limx→ 0

x2 x = lim 1

2x→0

= ½ Respuesta

35) limx→0

3 x2

6 sen2 x= 3(0)2

6 sen20 = 00→indeterminacion

limx→0

3 x2

6 sen2 x=limx→0

3 x2

6 sen x . sen x=

limx→0

3 x2

6 sen xx. x sen x

x. x=

limx→ 0

(3 x2 )

limx→0 (6 sen xx . x sen x

x. x) =

limx→0

(3 x2 )

limx→0 (6 sen xx . x) lim

x→0 (6 sen xx . x) =

limx→ 0

(3 x2 )

( limx→ 06)( lim

x→0sen x

x ) (limx→0x )( lim

x→0sen x

x )( limx→0x )

= limx→0

(3 x2 )

limx→ 0

(6 ) ( limx→0x) (limx→ 0

x )=

limx→0

(3 x2 )

limx→0

(6 )(limx→0x2)

=

6 limx→0

(3 x2 )

( limx→ 0x2) =

6 limx→0

(3 x2 )

x2 = 6 (3) = 18 Respuesta