WorkSheet 3

Sets

a ) A 2 , 3 , 4 , 5

B 3 , 5 , 7 , 9

A U B 2 , 3 , 4 , 5 , 7 , 9

A ? B 3 , 5

A\B 2 , 4

B\A 7 . 9

A ? R 2 , 3 , 4 , 5

b ) [2 , 3]

[1 , 4]

[1 .2

Derivatives

a ) f (x x3

f (x lim f (x h ) - f (x

h ? 0 h

f (x lim (x h )3 - x3

h ? 0 h lim a3 3a2h 3ah2 h3

h ? 0 h lim 3a2 3ah h2

p h ? 0 3a2

b ) Prove : d /dx (a f (x a d /dx f (x

let g (x a f (x , where a is a constant

by definition , d /dx f (x f (x lim f (x h ) - f (x

h ? 0 h

g (x lim g (x h ) - g (x

h ? 0 h lim a ? f (x h ) - a f (x ) by substitution

h ? 0 h lim a ? [f (x h ) - f (x )] by factoring out a

h ? 0 h a ? lim f (x h ) - f (x ) by properties of limits

h ? 0 h a ? f (x ) by the definition given earlier

therefore , d /dx (a f (x a d /dx f (x

c ) Prove : d /dx (f g (x d /dx f (x d /dx g (x

let h (x (f g (x

by definition , d /dx f (x f (x lim f (x h ) - f (x

h ? 0 h

by definition , d /dx g (x g (x...