The value of the limit Limx→0 (cos x)cot2 x is
  • 1
  • e
  • e1/2
  • e-1/2
The value of limit Limx→0 {sin (a + x) – sin (a – x)}/x is
  • 0
  • 1
  • 2 cos a
  • 2 sin a
Limx→-1 [1 + x + x² + ……….+ x10] is
  • 0
  • 1
  • -1
  • 2
The value of Limx→01 (1/x) × sin-1 {2x/(1 + x²) is
  • 0
  • 1
  • 2
  • -2
Limx→0 log(1 – x) is equals to
  • 0
  • 1
  • 1/2
  • None of these
Limx→0 {(ax – bx)/ x} is equal to
  • log a
  • log b
  • log (a/b)
  • log (a×b)
The value of limy→0 {(x + y) × sec (x + y) – x × sec x}/y is
  • x × tan x × sec x
  • x × tan x × sec x + x × sec x
  • tan x × sec x + sec x
  • x × tan x × sec x + sec x
Limy→∞ {(x + 6)/(x + 1)}(x+4) equals
  • e
  • e³
  • e5
  • e6
The expansion of log(1 – x) is
  • x – x²/2 + x³/3 – ……..
  • x + x²/2 + x³/3 + ……..
  • -x + x²/2 – x³/3 + ……..
  • -x – x²/2 – x³/3 – ……..
If f(x) = x × sin(1/x), x ≠ 0, then Limx→0 f(x) is
  • 1
  • 0
  • -1
  • does not exist
The value of Limn→∞ {1² + 2² + 3² + …… + n²}/n³ is
  • 0
  • 1
  • -1
  • n
The value of Limn→∞ (sin x/x) is
  • 0
  • 1
  • -1
  • None of these
The value of Limx→0 ax is
  • 0
  • 1
  • 1/2
  • 3/2
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.
  • 0
  • 1
  • -1
  • None of these
Limx→0 sin (ax)/bx is
  • 0
  • 1
  • a/b
  • b/a
The value of the limit Limx→0 {log(1 + ax)}/x is
  • 0
  • 1
  • a
  • 1/a
If f(x) = (x + 1)/x then df(x)/dx is
  • 1/x
  • -1/x
  • -1/x²
  • 1/x²
Limx→0 (ex² – cos x)/x² is equals to
  • 0
  • 1
  • 2/3
  • 3/2
0 h : 0 m : 1 s

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