limθ→0 [4θ (tan θ – 2θ tan θ)] / (1 – cos 2θ) = 1) 1/√2 2) 1/2 3) 1 4) 2 Solution: (4) 2... View Article
limx→0 (√1 – cos 2x) / (√2 x) = 1) 2 2) -1 3) 0 4) does not exist Solution: (4) does not exist... View Article
limx→0 [ex – esinx] / [x – sin x] = 1) -1 2) 0 3) 1 4) None of these Solution: (3) 1... View Article
For x > 0, limx→0 [(sin x)1/x + (1 / x)sinx] = 1) 0 2) -1 3) 1 4) 2 Solution: (3) 1... View Article
The value of limɑ→0 [cosec-1 (sec ɑ) + cot-1 (tan ɑ) + cot-1 (sin-1 ɑ)] / ɑ is 1) 0 2) -1 3) -2 4) 1 Solution: (3) -2... View Article
The value of limx→0 [∫0x^2 sec2 t dt] / [x sin x] = 1) 3 2) 2 3) 1 4) 0 Solution: (3) 1... View Article
The value of limx→∞ [(Ï€ / 2) – (tan-1 x)]1/x = 1) 0 2) 1 3) -1 4) e Solution: (2) 1... View Article
limx→0 (d / dx) [∫(1 – cos x) / x2] dx = 1) 1 2) 0 3) 1/2 4) None of these Solution: (3) ½... View Article
limx→0 [(1 – cos 2x) sin 5x] / [x2 sin 3x] = 1) 10/3 2) 3/10 3) 6/5 4) 5/6 Solution: (1) 10/3... View Article
The value of limx→0 [1 + sin x – cos x + log (1 – x)] / x3 is 1) -1 2) 1/2 3) -(1/2) 4) 1 Solution: (3) -(1/2)... View Article