Graphics Reference
In-Depth Information
0as n
Provethat, for any given x ,( R
( x ))
.
Deduce that
exp( x )
x n ! .
Use computer graphics to observe the connection between the
graphs of y 1, y 1 x , y 1 x
x ,..., and y exp( x ).
39 Use Maclaurin's Theorem to say what you can about R
( x ) where
x 3! ... ( 1)
x
(2 n 1)! R
sin x x
( x ).
Provethat, for any given x ,( R
( x )) 0as n .
Deduce that
sin x
x
(2 n 1)! .
( 1)
Observe the connection between the graphs you drew for qn 16 and
this result.
40 Use Maclaurin's Theorem to say what you can about R
( x ).
x 2! ... ( 1)
x
(2 n )! R
cos x 1
( x ).
Provethat, for any given x ,( R
( x )) 0as n .
Deduce that
cos x
x
(2 n )! .
(
1)
Observe the connection between the graphs you drew for qn 16 and
this result.
41 If f ( x ) log(1 x ), useqn 1.8(i) to show that
( n 1)!
(1 x )
f ( x ) ( 1)
.
Use Maclaurin's Theorem to say what you can about R
( x ) where
x 2
x 3
x
n
x )
x
1 R
log(1
...
(
1)
( x ).
 
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