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NCERT Solutions for class 13 Maths | Chapter 13 - Introduction to Limits and Derivatives

Questions
1 Let f(x) = cos x, when x ≥ 0 and f(x) = x + k, when x < 0 Find the value of k given that Limx→0 f(x) exists
A 0
B 1
C -1
D None of these

Answer:1
2 The expansion of log(1 – x) is
A x – x²/2 + x³/3 – ……..
B x + x²/2 + x³/3 + ……..
C -x + x²/2 – x³/3 + ……..
D -x – x²/2 – x³/3 – ……..

Answer:-x – x²/2 – x³/3 – ……..
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3 The value of limit Limx→0 {sin (a + x) – sin (a – x)}/x is
A 0
B 1
C 2 cos a
D 2 sin a

Answer:2 cos a
4 The derivative of [1+(1/x)] /[1-(1/x)] is
A 1/(x-1)²
B -1/(x-1)²
C 2/(x-1)²
D -2/(x-1)²

Answer:1/(x-1)²
5 The value of the limit Limx→0 {log(1 + ax)}/x is
A 0
B 1
C a
D 1/a

Answer:0
6 If f(x) = x × sin(1/x), x ≠ 0, then Limx→0 f(x) is
A 1
B 0
C -1
D does not exist

Answer:0
7 If f(x) = (x + 1)/x then df(x)/dx is
A 1/x
B -1/x
C -1/x²
D 1/x²

Answer:-1/x²
8 The value of Limn→∞ (sin x/x) is
A 0
B 1
C -1
D None of these

Answer:0
9 The value of limy→0 {(x + y) × sec (x + y) – x × sec x}/y is
A x × tan x × sec x
B x × tan x × sec x + x × sec x
C tan x × sec x + sec x
D x × tan x × sec x + sec x

Answer:x × tan x × sec x + sec x
10 The value of Limx→01 (1/x) × sin-1 {2x/(1 + x²) is
A 0
B 1
C 2
D -2

Answer:2
11 The value of Limx→0 ax is
A 0
B 1
C 1/2
D 3/2

Answer:1
12 Limx→0 (ex² – cos x)/x² is equals to
A 0
B 1
C 2/3
D 3/2

Answer:3/2
13 The value of the limit Limx→0 (cos x)cot2 x is
A 1
B e
C e1/2
D e-1/2

Answer:e-1/2
14 Limx→0 {(ax – bx)/ x} is equal to
A log a
B log b
C log (a/b)
D log (a×b)

Answer:log (a/b)
15 Limx→-1 [1 + x + x² + ……….+ x10] is
A 0
B 1
C -1
D 2

Answer:1
16 Limy→∞ {(x + 6)/(x + 1)}(x+4) equals
A e
B e³
C e5
D e6

Answer:e5
17 The value of Limn→∞ {1² + 2² + 3² + …… + n²}/n³ is
A 0
B 1
C -1
D n

Answer:0
18 The value of Limx→0 (1/x) × sin-1 {2x/(1 + x²) is

A 0
B 1
C 2
D -2

Answer:2
19 Limx→0 sin (ax)/bx is
A 0
B v
C a/b
D b/a

Answer:a/b
20 Limx→0 log(1 – x) is equals to
A 0
B 1
C 1/2
D None of these

Answer:0

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