MTH101 Final Term Solved Papers Set 2

6    7 8 " 57 8 ( 0  !  

x y =



 


  

y



x
 

 
6    7  " 57 8 ( 0  !  

x y

dy dx = 6    7 9 " 57 8 ( 0  !   


 


  


 
!



7

x = x = x

and x x = 6    7 : " 57 8 ( 0  !  

n n +

1)(

2) n

n 2) n n +

1) n n + 6    7 ; " 57 8 ( 0  !  

1 [ ( )] L

f x

dy 1 [ b a L

f x 1 [ L

f x dy 1 [ L

f x dx 6    7 < " 57 8 ( 0  !   )
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6    7 = " 57 8 ( 0  !  








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6    7 ? " 57 8 ( 0  !   )



4 

y x

x
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6    7  " 57 8 ( 0  !   *!# 

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6    7 8 " 57 8 ( 0  !  

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%
6    7 88 " 57 8 ( 0  !  

(0,

int a

where a is any negative

eger 6    7 8 " 57 8 ( 0  !  

2 ) y

x

x (37)(

2 ) dy

x

x dx =

2 ) dy

x x

x dx =

(111

74)(

2 ) dy

x

x

x dx =

(111

74)(

2 ) dy

x

x

x dx = 6    7 89 " 57 8 ( 0  !   5 

 
 

x

x

dx x

x

x t x

x

x x

x

dx

dt x

x

x

t 6    7 8: " 57 8 ( 0  !   log b ac = log

log b

b a

c log

log b

b a

c log log b b a c log

log b

b a

c 6    7 8; " 57 8 ( 0  !   
 
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6    7 8< " 57 8 ( 0  !   )
7 
8  
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9
 




  

 



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:

f b

f a f c

b a f b

f a f c

b a f a

f b f c

b a f a

f b f c

b a 6    7 8= " 57 8 ( 0  !  

d F x

f x dx F x

C

6   









1









7 '# #
 
6    7 8? " 57 8 ( 0  !  

n

k

k k

f x

x

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1 #









 
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1 #
6    7 8 " 57 8 ( 0  !   cosu du π
8 6    7  " 57 8 ( 0  !   sinu du π 6    7 8 " 57 8 ( 0  !  

d F x

f x dx f x 

F x

C 
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