Ejercicios de cálculo del libro de Stewart

Ejercicios:

1)limh→0

¿ 2.7h−7h

y limh→0

¿ 2.8h−7h

2)

2.7h ln 2.7 (h )−(2.7h−7)(1)h2

2.8h ln 2.8(h)−(2.8h−7 )(1)

h2

3) 4)

5) 6)F ( x )=34x8=24

4x7=6 x7

7)F ( x )=x3−4 x+6 8)F (t )=1.4 t 5−2.5 t 2+6.7

F ' (x)=3x−4 F ' (t )=7 t 4−5 t

9)g ( x )=x2 (1−2x ) 10)h ( x )=(x−2)(2x+3)

g' (x )=2x (1−2 x )+x2(−2) h' ( x )=1 (2x+3 )+(x−2)(2)

11) g ( t )=2 t−34 12)B ( y )=c y−6

g' (t )=−34

(2 ) t−34

−1=−32t−74 B' ( y )=−6c y−7

13)A ( s)=−12s5

14)y ( x )=x53−x

23

A ' (s)(0 ) ( s5 )+(12)(5 s4)

(s¿¿5)2¿ 5

3x23−23x

−13

15) R (a )=(3a+1)2 16)h (t )=4√ t−4 et

2(3a+1)(3) h' ( t )=t14=14t−34

17)s ( p )=√ p−p 18)y ( x )=√ x( x−1)

s' (p )=p12−p=

12p

−12 −1 y ' (x )= x

12 (x−1)

y ' (x )=12x

−12 ( x−1 )+x

12

19) y (x )=3ex 43√ x

20)S (r )=4 π R2

y ' (x )=3ex+4 x−13 S' (r )=8 πR

y ' (x )=3ex−43x

−43

21)h (u )=Au3+Bu2+Cu 22)y (x )=√x+xx2

h' (u )=3 Au2+2Bu+c y ’ ( x )=

( 12 x−12 +1) (x2 )−(x

12+x )(2 x)

2x

23)y ( x )= x2+4 x+3

√x 24)g (u )=√2u+√3u

y ' (x )=(2 x+4 )(x

12 )−(x2+4 x+3)(1

2x

−12 )

√x2 g ’ (u )=√8+√3 1

2u

−12

25) j ( x )=x2.4+e2.4 26)K (r )=er+re

j' ( x )=2.4 x1.4+0 K ' (r )=er+e re−1

27)H ( x )=(x+x−1)3 28)y=aev+ bv+ cv2

3(x+x−1)(1−x−2) y ’=aev−b v−2−2c v−3

29)u (t )=t15+4 t

52 30)V ( x )=(√x+ 13√x )

2

u' ( t )=15t−14 +10 t

32 V ' (x )=2(√ x+ 1

3√ x)(12x

−12 −13x

−43 )

31)Z¿y

y10+Bey 32)Y=cx+1+1

Z’=−10 A y−11+Be y . ln Be Y '=e x (e )+ex .e=ex (e)