Continuity and Differentiability questions
732 published questions with worked solutions.
- If the function is defined as f(x) = 5^ x - 1 2 - x , when x 2 , = 2 5, when x = 2
- If f(x) = cases 5^x - e^x 2x , & x 0 [1mm] 1 2 ( 5 + 1), & x = 0 cases then
- A function f is said to be removable discontinuous at x = 0, if _ x 0 f(x) exists and
- The points at which the function f(x) = x + 1 x^2 + x - 12 is discontinuous, are
- Examine the continuity of the following function f(x) = x x - 3 x x^2 + 2 x , x 0 and f(x) = 1 at x = 0
- At which points the function f(x) = x [x] , (where [.] is greatest integer function), is discontinuous
- For the function f(x) = cases ^2 ax x^2 , & when x 0 1, & when x = 0 cases which one is a true statement
- The function x |x| is
- If f(x) = [ x 2 ] is discontinuous at x = a, then
- The points of discontinuity of the function f(x) = _ n (2 x)^ 2n 3^n - (2 x)^ 2n are given by
- If f(x) = |x| x , for x 0 = 0, for x = 0, then f(x) is
- If f(x) = cases 2^ 1 x , & for x 0 3, & for x = 0 cases , then
- If f(x) = ( 4 - x ) 2x (x 4 ) is everywhere continuous, then f ( 4 ) is equal to
- Let f(x) = 1 + x - 1 - x x . The value which should be assigned to f at x = 0 so that it is continuous everywhere is
- If f(x) = cases -x^2, & x 0 5x - 4, & 0 < x 1 4x^2 - 3x, & 1 < x < 2 3x + 4, & x 2 cases then f(x) is
- If f(x) = [e^2]x^2 - [-e^2]x^2 ^2 x , x 0 is continuous function, then f(0) is equal to
- Let f(x) = cases 5^ 1 x , & x < 0 [x], & x 0, R cases , then at x = 0
- The function f(x) = x^2 - 10x + 26 x^4(x^2 - 9)(1 + 27x^2) is continuous for
- If f(x) = cases x + 2, & when x < 1 4x - 1, & when 1 x 3 x^2 + 5, & when x > 3 cases then the correct statement is
- If f(x) = cases ( x^2 a ) - a, & when x < a 0, & when x = a a - ( x^2 a ), & when x > a cases , then
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