If limx→0 [(ekx – 1) sin kx] / x2 = 4, then k = 1) 2 2) -2 3) ± 2 4) ± 4 Solution: (3) ± 2... View Article
The value of limx→0 [1 – cos (1 – cos x)] / x4 is 1) 1/2 2) 1/4 3) 1/6 4) 1/8 Solution: (4) â…›... View Article
The value of limx→0 [sin2 x + cos x – 1] / x2 = 1) 1 2) 1/2 3) - (1/2) 4) 0 Solution: (2) ½... View Article
limx→0 [sin |x|] / x = 1) 1 2) 0 3) positive infinity 4) does not exist Solution: (4) does not exist... View Article
The value of limx→π/2 [sin (cos x) (cos x)] / [sin x – cosec x] is 1) ∞ 2) 1 3) 0 4) -1 Solution: (4) -1... View Article
limx→2 [(√1 – {cos 2 (x – 2)}) / (x – 2)] = 1) √2 2) -√2 3) 1/√2 4) does not exist Solution: (4) does not exist... View Article
Let f (x) = ∫1x sin t / (t) dt, limx→∞ f’ (x) = 1) 0 2) 1 3) 2 4) None of these Solution: (1) 0... View Article
limx→0 [(2 + x) sin (2 + x) – 2 sin 2] / x = 1) sin 2 2) cos 2 3) 1 4) 2 cos 2 + sin 2 Solution: (4) 2 cos 2 + sin 2... View Article
limx→0 [(1 + tan x) / (1 + sin x)]x = 1) 1/e 2) 1 3) e 4) e2 5) None of these Solution: (2) 1... View Article
limx→0 [(1 – cos 2x) (3 + cos x)] / [x tan 4x] = 1) - (1/4) 2) 1/2 3) 1 4) 2 Solution: (4) 2... View Article
The value of limx→0 [∫0x cos t dt] / x = 1) 1 2) -1 3) ∞ 4) None of these Solution: (1) 1... View Article
If limx→0 [2a sin x – sin 2x] / [tan3 x] exists and is equal to 1, then the value of a is 1) 2 2) 1 3) 0 4) -1 Solution: (2) 1... View Article
limx→π/2 [(1 – tan (x / 2) (1 – sin x)] / [(1 + tan (x / 2) (Ï€ – 2x)3] = 1) 1/8 2) 0 3) 1/32 4) ∞ Solution: (3) 1/32... View Article
limx→tan^(-1) 3 [(tan2 x – 2 tan x – 3) / (tan2 x – 4 tan x + 3)] = 1) 1 2) 2 3) 0 4) 3 Solution: (2) 2... View Article
For x belongs to R, limx→∞ [(x – 3) / (x + 2)]x = 1) e 2) e-1 3) e-5 4) e5 Solution: (3) e-5... View Article
If f(a) = 2, f ‘ (a) = 1, g(a) = 3, g ‘(a) = -1 then limx→a [f (a) g (x) – f (x) g (a)] / (x – a) = 1) 6 2) 1 3) -1 4) -5 Solution: (4) -5... View Article