Question 1: If , then find the values of x satisfying the equation.
.
Answer:
Given
Given
Question 2: If , find
.
Answer:
Given
Question 3: If
, show that
.
Answer:
Given
. Hence proved.
Question 4: If
, show that
Answer:
. Hence proved.
Question 5: If
show that
.
Answer:
Given
. Hence proved.
Question 6: If
Find i) ii)
iii)
iv)
v)
Answer:
Given
i)
[ Using
]
ii) [ Using
]
iii)
[ Using
]
iv) does not exist since
is not defined in
.
Question 7: If
show that
Answer:
Given
Question 8: If
, show that
Answer:
Given
Question 9: If
, then show that:
i)
ii)
Answer:
Given
i)
ii)
Question 10: If and
, then prove that
for all
Answer:
Given and
Hence for all
Question 11: If for non-zero
, where
, then find
.
Answer:
Given
… … … … … i)
… … … … … ii)
Adding i) and ii)
… … … … … iii)
Subtracting ii) from 1
… … … … … iv)
Adding iii) and iv) we get