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

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