Page 91 - Mathematics Class - XI

Viva-Voce

1. What is meant by limit of a function?
Ans. Limit of a function at a point is the common value of the left and right hand limits, if they coincide.

2. What do you mean by “x tends to c”?
Ans. “x tends to c (x → c)” means x takes the values very close to c but x ≠ c.
3. What do you mean by left hand limit of a function f(x)?

Ans. Left hand limit of a function f(x) is that value of f(x) which is dictated by the values of f(x) when x tends
to a from the left.

2
4. Find: lim x − 4
x→2 x + 3
−
2
x − 4 44 0
Ans. lim = = = 0
+
x→2 x + 3 23 5
5. What do you mean by right hand limit of a function f(x)?
Ans. Right hand limit of a function f(x) is that value of f(x) which is dictated by the values of f(x) when x tends
to a from the right.
6. What is the value of lim(sin) ?
0
Ans. 0

MCQs

sin x
1. The value of lim is
x x
a) 1 b) 2 c) –1 d) –2
sin x
2. The value of lim is
x→0 x
a) 1 b) –1 c) 0 d) does not exist

3. The value of lim a x sin b where a, b > 1 is
x
x a
a) b b) a c) a log b d) b log a
e
e

sin x
4. lim 3 equal to

x 2 cos x 1
3
a) 3 b) 1 c) 1 d) 3
2 3 2

Answers: 1. a) 1 2. d) does not exist 3. a) b 4. c) 1
3
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