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

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Questions
1 Limx->∞ {(x + 6)/(x + 1)}(x + 4) equals
A e
B e3
C e5
D e6

Answer:e5
2 Limx->0 (1 - cos x)/x is
A 0
B 1
C 1/2
D Limit does not exist

Answer:0
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3 Limx->0 sin (ax)/bx is
A 0
B 1
C a/b
D b/a

Answer:a/b
4 Then value of Limx->0 {ex - (1 + x)}/x2 is
A 0
B 2
C 1/2
D e

Answer:1/2
5 The value of the limit Limn->∞ (1 + 1/n)n+5 is
A 0
B 1
C e
D 1/e

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

Answer:a
7 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:-2/(x-1)2
8 The value of limx->0 {(x3 * cotx)/(1-cosx)} is
A 0
B 1
C -1
D 2

Answer:2
9 The expansion of ex is
A ex = 1 - x/1! + x2 /2! - x3 /3! + x4 /4! - ..............
B ex = 1 + x/1! + x2 /2! + x3 /3! + x4 /4! + ..............
C ex = -1 - x/1! - x2 /2! - x3 /3! - x4 /4! - ..............
D None of these

Answer:ex = 1 + x/1! + x2 /2! + x3 /3! + x4 /4! + .............
10 The derivative of x + 1/x is
A 1 + 1/x
B 1 - 1/x
C 1 - 1/x2
D 1 + 1/x2

Answer:1 - 1/x2
11 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
12 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 - ........
13 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)
14 The value of Limx->∞ (sin x/x) is
A 0
B 1
C -1
D None of these

Answer:0
15 Limx->-1 [1 + x + x2 + ..........+ x10 ] is
A 0
B 1
C -1
D 2

Answer:1
16 The value of Limx->a (a*sin x - x*sin a)/(ax2 - xa2 ) is
A (a*cos a + sin a)/a2
B (a*cos a - sin a)/a2
C (a*cos a + sin a)/a
D (a*cos a - sin a)/a

Answer:(a*cos a - sin a)/a2
17 The value of Limx->0 (sin ax/sin bx) is
A a+b
B a-b
C a*b
D a/b

Answer:a/b
18 The value of Limx->0 (1 + x)n is equal to
A 0
B 1
C 1/2
D None of these

Answer:1
19 The value of the limit Limn->0 (1 + an)b/n is
A ea
B eb
C eab
D ea/b

Answer:eab
20 The expansion of ax is
A ax = 1 + x/1! * (log a) + x2 /2! * (log a)2 + x3 /3! * (log a)3 + ...........
B ax = 1 - x/1! * (log a) + x2 /2! * (log a)2 - x3 /3! * (log a)3 + ...........
C ax = 1 + x/1 * (log a) + x2 /2 * (log a)2 + x3 /3 * (log a)3 + ...........
D ax = 1 - x/1 * (log a) + x2 /2 * (log a)2 - x3 /3 * (log a)3 + ...........

Answer:ax = 1 + x/1! * (log a) + x2 /2! * (log a)2 + x3 /3! * (log a)3 + ...........

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