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Class 11
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Maths
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Limits and Derivatives
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1.
The value of the limit Lim
x→0
(cos x)
cot2 x
is
A
1
B
e
C
e
1/2
D
e
-1/2
2.
The value of limit Lim
x→0
{sin (a + x) – sin (a – x)}/x is
A
0
B
1
C
2 cos a
D
2 sin a
3.
Lim
x→-1
[1 + x + x² + ……….+ x
10
] is
A
0
B
1
C
-1
D
2
4.
The value of Lim
x→01
(1/x) × sin
-1
{2x/(1 + x²) is
A
0
B
1
C
2
D
-2
5.
Lim
x→0
log(1 – x) is equals to
A
0
B
1
C
1/2
D
None of these
6.
Lim
x→0
{(a
x
– b
x
)/ x} is equal to
A
log a
B
log b
C
log (a/b)
D
log (a×b)
7.
The value of lim
y→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
8.
Lim
y→∞
{(x + 6)/(x + 1)}
(x+4)
equals
A
e
B
e³
C
e
5
D
e
6
9.
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 – ……..
10.
If f(x) = x × sin(1/x), x ≠ 0, then Lim
x→0
f(x) is
A
1
B
0
C
-1
D
does not exist
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Practice more on Limits and Derivatives
Quiz 1
Quiz 2