Basic mathematics for physics in class 11.pdf

Physics 11

1. BASIC MATHEMATICS FOR PHYSICS

2. 2 2 2
() 2abaabb 22
()()ababab 2 2 2
() 2abaabb

7. 3 3 3
() 3()abababab 3 3 3
() 3()abababab

8. 3 3 2 2
()( )ababaabb 3 3 2 2
()( )ababaabb

9. 1/3 2/3 3 2
155, 3126.Ifx thenfindthevalueofxxx 

10. 3
28

11. log1
a
a log
n
a
an

12. log
a
b
ab

13. ,loglog
mn
ifmnthenaa 24
log16log16Showthat 

14. log10
a


15. log()loglog
m m m
ab ab log(15)
m


16. log loglog
m m m
a
ab
b



 15
log
8
m





17. log
log
log
a
m
a
n
n
m
 1
log
log
n
m
m
n


18. logloglog
b c c
aba

21. log 10.withbase log20
log200
log0.2
log0.02





39. (3,0)A (0,4)B

46. 11
(,)xy

48. 11
(,)xy 22
(,)xy

51. 0axbyc નેસમ ાંતરઅનેબ ાંદુ11
(,)xy મ ાંથીપસ રથતીરેખ નુાંસમીકરણ

54. 0axbyc નેલાં અનેબ ાંદુ11
(,)xy મ ાંથીપસ રથતીરેખ નુાંસમીકરણ

56. 0axbyc 11
(,)Pxy

66. 11 22
0 1 2
() ... ...
n n n n n n n n nrr n n
rn
xaCxCxaCxa Cxa Ca
  
    !
!()!
n
r
n
C
rnr

 !(1)(2)...321nnnn

67. 2
()xa

68. 3
()xa

69. 4 4 3 22 3 4
() 464xaxxaxaxaa

70. (1)
n
x

71. 23(1)(1)(2)
(1)1 ...
2! 3!
n nn nnn
x nx x x
 
  

72. (1)1
n
x nx

 (1)1
n
x nx

 1Forx

73. 1
3
(1001)

83. 22
sincos1

84. 22
sectan1

85. 22
seccot1co

87. (1)sin()sincoscossin
(2)sin()sincoscossin
(3)cos()coscossinsin
(4)cos()cossinsinsin
ABABAB
ABABAB
ABABAB
ABABAB
 
 
 
 

88. tantan
tan()
1tantan
AB
AB
AB


 tantan
tan()
1tantan
AB
AB
AB




89. sin2.....A

90. cos2.....A

91. tan2.....A

92. sin75.....
o


93. tan15.....
o


96. (,)Pxy  O

97. (,)Pxy  O

98. (,)Pxy  O

99. (,)Pxy

108. sin120......
o
 cos120......
o


109. sin300......
o
 cos300......
o


110. tan315......
o


111. 22
sin135sec135......
oo


119. y
x



120. 0
d
a
dx


121. 1
d
x
dx


122. 1nnd
axnax
dx



123. xxd
ee
dx


124. 1
ln
d
x
dxx
 1
loglog
aa
d
xe
dx x


125. sincos
d
xx
dx


126. cossin
d
xx
dx


127. 2
tansec
d
xx
dx


128. 2
cotcos
d
x ecx
dx


129. cos coscot
d
ecx ecxx
dx


130. 1
2
1
sin
1
d
xdx
dx x


 1
2
1
cos
1
d
xdx
dx x
 



131. 1
2
1
tan
1
d
xdx
dx x


 1
2
1
cot
1
d
xdx
dx x
 



132. 1
2
1
sec
1
d
xdx
dx xx


 1
2
1
cos
1
d
ecxdx
dx xx
 



133. 1 1 1
4 2 4
(1)(1)(1)yxxx .....
dy
dx


134. sin..........
d
x
dx


135. 2
sin(1)..........
d
x
dx


136. 2
sin
..........
xd
e
dx


137. logsin...........
xd
e
dx


138. ()()()()
d d d
fxgxfxgx
dx dx dx
 

139. ()()()()()()
d d d
fxgxfxgxfxgx
dx dx dx
 

141. 2
()()()()
()
() [()]
dd
gxfxfxgx
dfx dx dx
dxgx gx



142. 2
2
1
dx
dxx

146. ()()
d
fxgx
dx
 ()()gxdxfxc

147. 1
log||dxxc
x
 xx
edxec log
x
x
e
a
adx c
a


148. sin cosxdx xc cossinxdxxc

149. sectansecxxdxxc 2
sec tanxdxxc seccot seccoxxdxcoxc  2
sec cotcoxdx xc

150. 3
(1)x
dx
x



151. 22
seccosxecxdx

152. 1
1sin
dx
x


153. 3
2
(8)(1)
24
xx
dx
xx




154. 2
2
(1)
x
dx
x




155. 813
47
x
dx
x




156. '()[()]()()
b
b
a
a
fxdxfxfbfa 

157. 2
.....
b
a
xdx

158. sin.....
b
a
xdx

159. 1
.....
b
a
dx
x
