Continuity: JEE Questions & Solutions

Let f(x) = cases ax^2 + 2ax + 34x^2 + 4x - 3, & x - 32, 12 b, & x = - 32, 12 cases be continuous at x = - 32. If f(x) = 75, then x is equal…

If f(x) = cases a|x| + x^2 - 2( |x|)( |x|)x &, x 0 b &, x = 0 cases 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)= cases b^2 [ 2 [ 2( x+ x) x ] ], & x<0 x- 12 2xx^3, & x0…

Let f(x)= 0 ( x-) (x-1) 1+x^ /2(x-1), x R. Consider the following statements: [(I)] f(x) is continuous at x=1. [(II)] f(x) is continuous at…

If the function f(x)= cases 2x (k1 + 1)x + (k2 -1)x, & x < 0 4, & x = 0 2x e ( 2 + k1 x2 + k2 x), & x 0 cases is continuous at x = 0, then…

Let f(x) be defined as follows: f(x) = cases 3x, & if x < 0 (1+x+ x, 2+x x), & if 0 x 2 5, & if x 2 cases where. denotes the greatest…

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

The number of points of discontinuity of the function f(x) = x^22 - x, x [0, 4], where denotes the greatest integer function, is:

Consider f(x)= a(7x-12-x^2), b x^2-7x+12 for continuity. Find n(S).

Let f: R R be a function given by: 1 - (2x)x^2, for x < 0 1 - (x)x, for x 0. If f is continuous at x = 0, then ^2 + ^2 is equal to:

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

If the function f(x) = cases (1 + | x|)^ / | x|, & 0 < x < 2, & x = 2 e^ 6x 4x, & 2 < x < cases is continuous at x = 2, then 9 + 6 e + ^6 -…

Let f, g and h be the real valued functions defined on R as f(x) = arrayll x|x|, & x 0 array.

Let f(x) = x^2 - 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)= 1+x+[x], 2+x, x+2[x], 0 x 2. Let m be the number of points in [0,2], where f is not…