Page 41 - Mathematics Class - XII

Viva-Voce

1. What is limit of a function?
Ans. A function is said to have a limit l at a if it is possible to make the function arbitrarily close to l by
choosing values closer and closer to a. Note that the actual value at a is irrelevant to the value of the limit.
Notation: lim f (x) = l, which is read as “the limit of f (x) as x approaches to a is l ”.
x→ a
2. When is a function said to be continuous?
Ans. A function f (x) is said to be continuous at a point x = a, if lim fx lim fx fa
()
( )
()
x a x a
3. What is the meaning of right hand limit in function?
Ans. Right hand limit of f (x) as x tends to a exists and is equal to l, if as x approaches a through values greater
than a, the value of f (x) approaches a unique real number and we write
lim f (x) = l
x a
20
4. Find lim x 1 .
10
x 1 x 1
2 2 x 1 x 1
10
10
10
20
x 1 x 1 10
1
Ans. lim lim lim lim x 12
1
10
10
x 1 x 1 x 1 x 1 x 1 x 10 1 x 1
MCQs

xK, x 3
1. If function, fx() , 4 x 3 is continuous at x = 3, then the value of K will be

3 x 5 , x 3
a) 4 b) 2 c) 1 d) 3

sin 2 x
2. The value of K for which function fx() x , x 0 will be continuous at point x = 0

K, x 0
1 1
a) 2 b) c) –2 d) – 2
2
1
x
3. If fx() xsin, x 0 is continuous at x = 0, then the value of K will be

K, x 0

a) 1 b) 0 c) 2 d) –1
x 2
4. If f (x) = 2x and g(x) = + 1 then which of the following function is discontinuous.
2
g (x)
a) f (x) – g (x) b) f (x) + g (x) c) f (x) g (x) d)
f (x)

g (x)
Answers: 1. c) 1 2. a) 2 3. b) 0 4. d)
f (x)

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