Analysis and Approaches for IBDP Maths Ebook 2 | Page 138

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 42
1. Prove by mathematical induction that
( n
f
) ( x ) represents the
th
n derivative of
f
( n)
n
( �5) n!
�
( x)
� where n� and
n 1
(1 � 5 x)
�
1
f( x)
� 1 � 5x
.
[7]
2. Prove by mathematical induction that
( n
f
) ( x ) represents the
th
n derivative of
3. Prove by mathematical induction that
n � 2 and
( n
f
) ( x ) represents the
�
� � � � where n� and
( n) 2 x
f ( x) ( n( n 1) 2 nx x ) e
f ( x)
2 x
� x e .
( n) x n�1
x n
�
f ( x) �n7 (ln7) � x7 (ln7) where n� ,
f x
� x .
th
n derivative of ( ) 7 x
4.
n�1
1
( ) ( 1) (2 )! n
n � n
� �
2
Prove by mathematical induction that f ( x) � (1 � x)
where n� 2n
2 n!
�
and
( n ) th
1
f ( x ) represents the n derivative of f( x)
��
1� x
[8]
[7]
[7]
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