Continuity: JEE Questions & Solutions

Let f(x) = (ax² + 2ax + 3)/(4x² + 4x - 3), x ≠ -3/2, 1/2 b, x = -3/2, 1/2 be continuous at x = -3/2. If f(f(x)) = 7/5, then x is equal to:

If f(x) = (a|x| + x² - 2(sin|x|)(cos|x|))/x, x ≠ 0 b, x = 0 is continuous at x=0, then a+b is equal to

Let [t] denote the greatest integer less than or equal to t. If the function f(x)= b²sin [π/2[π/2(cos x+sin x)cos x]], x<0 (sin x-1/2sin…

Let f(x)=lim_(θ→ 0) (cos π x-x^(2/θ) sin(x-1))/(1+x^(2/θ)(x-1)), x∈ℝ. Consider the following statements: [(I)] f(x) is discontinuous at…

If the function f(x)= 2/x { sin(k₁ + 1)x + sin(k₂ -1)x }, x < 0 4, x = 0 2/x logₑ ( (2 + k₁ x)/(2 + k₂ x)), x > 0 is continuous at x = 0,…

Let f(x) be defined as follows: f(x) = 3x, if x < 0 min(1+x+⌊ x ⌋, 2+x⌊ x ⌋), if 0 ≤ x ≤ 2 5, if x > 2 where ⌊. ⌋ denotes the greatest…

Let f(x) = (1+ax)^(1/x), x < 0 1+b, x = 0 ((x+4)^(1/2) - 2)/((x+c)^(1/3) - 2), x > 0 be continuous at x = 0. Then e^a bc is equal to

The number of points of discontinuity of the function f(x) = ⌊ x²/2 ⌋ - ⌊ √x ⌋, x ∈ [0, 4], where ⌊ · ⌋ denotes the greatest integer…

Consider the function f(x)= a(7x-12-x²)/(b|x²-7x+12|), x<3 [6pt] 2^(sin(x-3)/(x-[x])), x>3 [6pt] b, x=3 where [x] denotes the greatest…

Let f: ℝ → ℝ be the function given by f(x) = (1 - cos 2x)/x², x < 0 α, x = 0 (β √(1 - cos x))/x, x > 0 where α, β ∈ ℝ. If f is continuous…

The set of all values of a for which lim_(x → a) ([ [x - 5] ] - [ [2x + 2] ]) = 0, where [ [x] ] denotes the greatest integer less than or…

Let f, g and h be the real valued functions defined on ℝ as f(x) = { x/|x|, x ≠ 0 1, x = 0. g(x) = { sin(x+1)/(x+1), x ≠ -1 1, x = -1. and…

Let f(x) = [ x² - x ] + | -x + [ x ] |, where x ∈ ℝ and [t] denotes the greatest integer less than or equal to t. Then, f is:

Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2, 1), where the function f(x) = |[x]| + √(x - [x]) is…

Let [x] denote the greatest integer function and f(x)=max{1+x+[x], 2+x, x+2[x]}, 0≤ x≤ 2. Let m be the number of points in [0,2], where f…