LIMITS CONTINUITYLIMITS, CONTINUITY AND
DIFFERENTIATION
Question 1
The functionQuestion 2
The function
( ) ( ) ( )log 1 log 1ax bxf x
+ − −
i d fi d h l hi h
( ) ( ) ( )f xx
=
is not defined at x = 0. The value which should be assigned to f at x = 0 so that it is gcontinuous at x = 0 is a) loga + logba) loga + logbb) 0) bc) a – b
d) a + b
If the function Question 3
1 cos x−⎧⎪ 2( ) 0f x for xx
k
⎪= ≠⎨⎪⎩
is continuous at x = 0 then the value of k is
k⎪⎩ X =0is continuous at x 0 then the value of k is
a)1 b)0c)1/2 d)-1
Question 4
− nxcos1=
→ mxnx
x cos1cos1lim
0 −→ mxx cos10
nma)
mnb)n m
c) 2m 2nd)c)2n
m2md)
Question 5
11
1a) b)x1− x1+
x
a) b)
c) d) 0x1x+
c) d) 0
Question 6
a) b)e9 e3a) b)
c) d) 0e9 e3
ec) d) 0e
Question 7
Question 8
If f:R→R is continuous such that f( + ) f( ) +f( ) ∀ R &f(x+y) = f(x) +f(y) ∀ x, y ∈R, &f(1) = 2 then f(100) =
a) b)0 100a) b)
c) d) 4000 100
200c) d) 400200
Question 9
where n is a non zero positive integer, th i l tthen a is equal to
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23Q
Question 24Q
Question 25Q
Question 26Q
Question 27Q
Question 28
Question 29Q
Question 30Q
Question 31Q
Question 32
Question 33Q
Question 34Q
Question 35Q
Question 36Q
Question 37Q
Question 38Q
Question 39Q
Question 40Q
Question 41Q
Question 42Q
Question 43Q
Question 44Q
Question 45Q
Question 46Q
Question 47Q
Question 48Q
Question 49Q
Question 50Q
Question 51Q
Question 52Q
Question 53Q
Question 54Q
Question 55Q
Question 56Q
Question 57Q
Question 58Q
Question 59Q
Question 60Q