If f(2) = 4 and f'(2) = 4. Then, limx→2 [x f (2) – 2 f (x)] / (x – 2) = 1) 2 2) -2 3) -4 4) 3 Solution: (3) -4... View Article
If f (x) = {1, when x is rational, 0 when x is irrational is, then limx→0 f (x) = 1) 0 2) 1 3) 1/2 4) None of these Solution: (4) None of these... View Article
limx→0 [ax + a-x – 2] / x2 = 1) (log a)2 2) log a 3) 0 4) None of these Solution: (1) (log a)2... View Article
limn→∞ [2-n (n2 + 5n + 6)] / (n + 4) (n + 5) = 1) 0 2) 1 3) ∞ 4) - ∞ Solution: (1) 0... View Article
limx→1 [e-x – e-1] / (x – 1) = 1) 1/e 2) - (1/e) 3) 1 4) None of these Solution: (2) - (1/e)... View Article
limx→∞ [(2x – 3) (3x – 4)] / [(4x – 5) (5x – 6)] = 1) 1/10 2) 0 3) 1/5 4) 3/10 Solution: (4) 3/10... View Article
The value of limx→∞ [(x2 + bx + 4) / (x2 + ax + 5)] is 1) b/a 2) 0 3) 1 4) 4/5 Solution: (3) 1... View Article
limx→0 [ax – bx] / (ex – 1) = 1) loge (a/b) 2) loge (b/a) 3) loge (ab) 4) loge (a+b) Solution: (1) loge (a/b)... View Article
The value of limx→∞ √a2x2 + ax + 1 – √a2x2 + 1 is 1) 1/2 2) 1 3) 2 4) None of these Solution: (1) ½... View Article
If f : R → R be a differentiable function having f (2) = 6, f'(2) = (1/48). Then limx→2 [∫6f (x) 4t3 dt] / [x – 2] = 1) 18 2) 12 3) 36 4) 24 Solution: (1) 18... View Article
The value of limx→∞ [(x2 – 2x + 1) / (x2 – 4x + 2)]x is 1) e2 2) e-2 3) e6 4) None of these Solution: (1) e2 This is of the form limx→∞ f(x)g(x). Here f(x) = (x2 - 2x + 1)/(x2 - 4x + 2) and... View Article
If f(x) differentiable and f” (0) = a, then limx→0 [2 f (x) – 3 f (2x) + f (4x)] / x2 = 1) 3a 2) 2a 3) 5a 4) 4a Solution: (1) 3a... View Article
If limx→∞ [(x3 + 1) / (x2 + 1)] – (ax + b) = 2, then 1) a = 1 and b = 1 2) a = 1 and b = - 1 3) a = 1 and b = -2 4) a = 1 and b = 2 Solution: (3) a = 1 and b = -2... View Article
limx→π/4 [∫2sec^2x f (t) dt] / [x2 – (Ï€2 / 16)] = 1) 8/Ï€ f(2) 2) 2/Ï€f(2) 3) 2/Ï€f(1/2) 4) 4f(2) Solution: (1) 8/Ï€ f(2)... View Article
Let f : R → R be a differentiable function and f (1) = 4, Then the value of limx→1 ∫4f (x) 2t / (x – 1) dt is 1) 8 f '(1) 2) 4 f '(1) 3) 2 f '(1) 4) f '(1) Solution: (1) 8 f '(1)... View Article