The Chemistry Maths Book, Second Edition

(Grace) #1

Solutions to exercises 637














Section 6.5




































Section 6.6






















68.tan


− 1

(x 1 + 1 2) 1 + 1 C














73.ln


tan


tan


12


12



















θ


θ


C







++


++















1


2


514


45


52


2

1

x


xx


tan (xC)


1


2


452 2


21

ln(xx++−) tan (x C++)



1


2


2


2


45


1

2

tan ( )



++






++










x +


x


xx


C


1


2


3


4


2

2

ln


x


x


C






















1


2


45


2

ln(xx C+++)


++




21 xC3 ln( )+


1


2


71262ln( )xx+− + ln( )




ln


()


()


x


x


C














4


3


2

1


7


21


3


ln


x


x


C



















1


2

T


12

3


/









kT


m


12

8


/









kT


πm


1


8


1


8


π


2


1


4


1


60


−+


8


315


cosx


C


−−


sin cos sin cos


42

105


4


315


xx xx


sin cos sin cos


63 6

921


xx xx












n


n


xdx


n

1
2

Zsin


Zsin sin cos


nn

xdx


n


=− xx



1


1

1


13


() 23 −



e


π

e


ab


abxbbxC


ax

()


(cos sin )


22





++


−+ +



1


5


(sin22 2xxeCcos )


x





75.ln 1 (1 1 + 1 tan 1 θ 2 2) 1 + 1 C


Chapter 7


Section 7.2


1.u


r

1 = 111 + 13 r; 1 u


r

1 = 1 u


r− 1

1 + 1 3, u


0

1 = 11


2.u


r

1 = 13


r

; 1 u


r

1 = 13 u


r− 1

, u


0

1 = 11
























  1. 1 , 3 , 5 , 11 , 21 , 43






10.u


n

1 = 1 u


0

, all n 11. 0 12.∞



  1. 0 14. 1 15. 0

  2. 325 17. 2


Section 7.3



  1. (i)n(2n 1 − 1 1) (ii) 190

  2. (i) (ii)− 195

  3. (i) (ii) 29524

  4. (i)


(ii)









  1. 11 + 15 x 1 + 110 x


2

1 + 110 x


3

1 + 15 x


4

1 + 1 x


5


  1. 11 + 17 x 1 + 121 x


2

1 + 135 x


3

1 + 135 x


4

1 + 121 x


5

1



  • 17 x


6

1 + 1 x


7


  1. 1 , 3 , 3 , 1 27. 1 , 4 , 6 , 4 , 1

  2. 1 , 7 , 21 , 35 , 21 , 7 , 1


x


x


x


n

12


12














()
xx

x


32 n

2

1


1


()−



1


2


3


1


3


1 499975


9










≈.


3


2


1


1


3





















n

1


2


() 31


n


n


n


2


()11 5−


1


1


2


1


2


5


2


13


2


29


2


, ,−,−,− ,−


1


1


2


1


6


1


24


1


120


1


720


,,, , ,


1


3


1


8


1


15


1


24


1


35


1


48


,, , , ,


1


2


3


4


9


8


27


16


81


32


243


,,, , ,


0


1


2


1


3


2


2


5


2


,,, ,,


uu


u


u


r

r

r

r

=−










=− =



1


55


1


1

0

; ,


1


2


22


1

tan ( tan )



θ +C

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