problemas del 11- al 20 (joel martínez)

7/25/2019 Problemas Del 11- Al 20 (Joel Martnez)

1/4

11)f(x )=

x+1x1

; P (1,0 )

m=limh 0

1+h+11+h1

0

h =limh 0

h

2+hh =limh 0

1

2+h= 1

2+0=12

m1=12

y0=12

(x+1 ) y=12

x1

2(Ecuacinde la recta tangente)

Ecuacin de la recta normal)

m2=2 y0=2 (x+1 ) y=2x+2

12) f(x )=x2+3; P (1,2 )

m=limh 0

(1+h )2+32

h =lim

h 0

1+2h+h2+32h

1+2h+h2+3+2

1+2h+h2+3+2=

limh 0

1+2h+h2+34

h (1+2h+h2+3+2)=

limh 0

4+2

h (1+2h

m1=1

2 y2=

1

2(x1) y=

1

2x+

3

2(Ecuacin de larectatangente )

m2=2 y2=2 (x1 ) y=2x+4 (Ecuacinde la recta normal)

13) f(x )=2x2+x+1; P (1,2 )

m=limh 0

2 (1+h )2+ (1+h )+12

h =lim

h 0

2(1+2h+h)2+1+h+12h

2(1+2h+h)2+1+h+1+2

2(1+2h+h)2+1+h+1+2=lim

h 0 h

m1=5

4 y2=

5

4(x1 ) y=

5

4x+

3

4(Ecuacin de larecta tangente)

m2=45

y2=45

(x1 ) y=45

x+14

5 (Ecuacinde la recta normal)

14) f(x )=

2x

x+1; P (1,1 )


2/4

m=limh 0

2(1+h)1+h+1

1

h =lim

h 0

2+2h2+h

1

h =lim

h 0

2+2h2h2+h

h =lim

h 0

h

2+hh =lim

h 0

1

2+h=

1

2+0=

1

2

m1=1

2 y1=1

2 (x1) y=1

2x+1

2 (Ecuacin de larectatangente)

m2=2 y1=2 (x1 ) y=2x+3(Ecuacin de la rectanormal)

15) f(x )= x2

x+2; P (2,1 )

m=limh 0

(2+h)2

2+h+21

h =lim

h0

4+4 h+h2

4+h 1

h =lim

h 0

4+4 h+h24h4+h

h =lim

h 0

h (3+h )4+h

h =lim

h 0

3+h4+h

=3+04+0

=3

4

m1=3

4 y1=

3

4(x2 ) y=

3

4x

1

2(Ecuacinde la recta tangente)

m2=43

y1=43

(x2 ) y=43

x+11

3 (Ecuacin de la rectanormal )

16) f(x )=x3+x1 ; P (2,9)

h

h( 2+6h+13)h

=limh 0

h2+6h+13=0+0+13=13

m=limh 0

(2+h)3

+ (2+h )19h

=limh 0

8+12h+6 h2+h3+2+h19h

=limh 0

13h+6h2+h3+1010h

=limh 0

m1=13 y9=13 (x2 ) y=13x17(Ecuacin de larecta tangente)


3/4

m2=113

y9=113

(x2 ) y=113

x+119

13(Ecuacin de la rectanormal )

17) f(x )= 1

x+1

; P(0,1)

m=limh 0

1

(0+h )+11

h =lim

h 0

1

h+11

h

1

h+1+1

1

h+1+1

=limh 0

1

h+11

h( 1h+1+1)=lim

h 0

1h1h+1

h( 1h+1+1)=lim

h 0

h+

h ( h+

m1=12

y1=12

(x0 ) y=12

x+1(Ecuacin de la recta tangente)

m2=2 y1=2 (x0 ) y=2x+1(Ecuacinde la recta normal)

18) f(x )= 4

2x+2; P(1,1)

m=limh 0

4

2(1+h)+21

h =lim

h 0

4

2+2h+21

h

4

2+2h+2+1

4

2+2h+2+1

=limh 0

4

2+2h+21

h

( 4

2+2h+2 +1)

=limh 0

444+2

h

( 4

2+2h

m1=14

y1=14

(x1 ) y=14

x+5

4(Ecuacinde larecta tangente)


4/4

m2=4 y1=4 (x1 ) y=4x3(Ecuacin de larecta normal)

19)f(x )=1

1

x; P(1,0)

m=limh 0

1 1

1+h0

h =lim

h 0

1+h11+h

h =lim

h 0

h

1+hh =lim

h 0

1

1+h=

1

1+0=1

m1=1 y0=1 (x1 ) y=x1(Ecuacin de la rectatangente )

m2=1 y0=1 (x1 ) y=x+1(Ecuacin de larecta normal)

20)f(x )= x

x21

; P(2,23 )

m=limh 0

2+h

(2+h )21

2

3

h =lim

h 0

2+h4+4h+h21

2

3

h =lim

h 0

6+3h88h2h2+29+12h+3h2

h =lim

h 0

665h2h2

9+12h+3h2

h =

m1=59

y2

3=59

(x2 ) y=59

x+16

9 (Ecuacinde larecta tangente)

Ecuacinde la recta normal

m2=9

5 y

2

3=

9

5(x2 ) y=

9

5x

44

15

problemas del 11- al 20 (joel martínez)

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