7/30/2019 Formulario lmites y derivadas

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Prof.: Carlos Figueroa M.

Agosto de 2012

FORMULARIO DE LMITES Y DERIVADAS

LMITES ESPECIALES:

1. 01

lim = kx x

, 0>k . 2. 1sin

lim0

= x

x

x3. 0

cos1lim

0=

x

x

x

4.2

1cos1lim

20

=

x

x

x

5. 1tan

lim0

= x

x

x6. 1

1lim

0 =

x

ex

x

7. ax

ax

xln

1lim

0=

8. ex xx

=+

1

0)1(lim 9. e

x

x

x=

+

+

11lim

DERIVADAS FUNDAMENTALES: (Suponga que zes una funcin de x).

1. 0)'( =k , kconstante. 2. ')'( 1znzz nn =3.

z

zz

2

')'( =

4. ')()'( zeezz = 5. azaa zz ln')()'( =

6.z

zz

')'(ln =

7.az

zza

ln

')'(log = 8.

')(cos)'(sin zzz = 9. ')sin()'(cos zzz =

10. ')(sec)'(tan2 zzz = 11. ')csc()'(cot 2 zzz = 12. ')tan(sec)'(sec zzzz =

13. ')cotcsc()'(csc zzzz =14.

2

1

1

')'(sin

z

zz

= 15.

2

1

1

')'(cos

z

zz

=

16. 21

1

')'(tan

z

zz

+= 17. 2

1

1

')'(cot

z

zz

+

= 18.1

')'(sec

2

1

=

zz

zz

19.1

')'(csc

2

1

=

zz

zz 20.

dx

dz

dz

dy

dx

dy= : R-Cadena.

21. '')'( gfgf =

22. ')'( kfkf = , kconstante. 23. '')'( fggffg += 24. 2

'

''

g

fggf

g

f =

RELACIONES TRIGONOMTRICAS BSICAS:

1. 1cossin 22 =+ xx2.

x

xx

cos

sintan = 3.

x

xx

sin

coscot =

4. seccos

xx

=1

5.x

xsin

1csc =

6. 12 2+ =tg secx x

7. 1 2 2+ =cot cscx x 8. xxx cossin2)2sin( = 9. xxx 22 sincos)2cos( =

10.x

xx

2tan1

tan2)2tan(

= 11.

2

)2cos(1sin2

xx

= 12. cos

cos( )2

1 2

2x

x=

+

13.)2cos(1

)2cos(1tan2

x

xx

+

= 14.x

xx

2tan1

tan2)2sin(

+= 15.

x

xx

2

2

tan1

tan1)2cos(

+

=