Continuity and Differentiability questions
732 published questions with worked solutions.
- The function f(x) = 2x^2 + 7 x^3 + 3x^2 - x - 3 is discontinuous
- The number of points at which the function f(x) = (|x - 1| + |x - 2| + x), where x [0, 4] is not continuous, is
- If f(x) = cases ax^2 + b, & 0 x < 1 4, & x = 1 x + 3, & 1 < x 2 cases then the value of (a, b) for which f cannot be continuous...
- The set of points of discontinuity of the function f(x) = |x| is
- If f(x) = 1 1 - x , then the points of discontinuity of the function f[f f(x) ] are
- The function f(x) = 2[ sgn (2x)] + 2 has
- Which of the following functions have finite number of points of discontinuity in R (where [.] represents greatest integer...
- The number or points at which the function f(x) = 1 x - [x] ([ ] denotes the greatest integer function) is not continuous, is
- If f(0) = 0 and f(x) = 1 (1 - e^ - x ) for x 0. Then, only one of the following statements on f(x) is true. That is f(x) is
- The function f(x) = cases 5^ x - e^ ( 2 - x ) x , & x 2 [2mm] 5 - e, & x = 2 cases has a ......... discontinuity at x = 2 .
- There is a root for the equation x^3 - x - 1 = 0 between
- If f(x) be a continuous function and g(x) be discontinuous, then
- The function y = 3 x - |x - 1| is continuous at
- At x = 3, f(x) = cases x^5 - 243, & if x 3 x^3 - 27, & if x = 3 cases is
- The value of f(0), if f(x) = x 2x 3x 5x is continuous at x = 0 is
- f(x) = cases 5^ x - 1 2 - x , & x 2 [1mm] 5, & x = 2 cases at x = 2 is
- The function f(x) = x^3 + x^2 - 16x + 20 x - 2 is not defined at x = 2. In order to make f(x) continuous at x = 2, the value of...
- If f(x) = cases x + a 2 x, & 0 < x < 4 2x x + b, & 4 x 2 a 2x - b x, & 2 < x cases is continuous at x = 4 , then a - b is equal to
- For what value of k, function f(x) = cases k x - 2x , & if x 2 [1mm] 3, & if x = 2 cases is continuous at x = 2 ?
- For what value of k, f(x) = cases 2^ x+2 - 16 4^x - 16 , & x 2 k, & x = 2 cases is continuous at x = 2?
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