Continuity and Differentiability questions
732 published questions with worked solutions.
- If f(x) = cases 3x + 5, & for -3 x < 3 2x + 8, & for 3 x < 5 x + 13, & for 5 x 7 cases is
- If f(x) = cases x^2, & when x 0 1, & when 0 < x < 1 1 x , & when x 1 cases , then f(x) is
- If f(x) = |x|, then f(x) is
- If f and g are both continuous at x = a, then f - g is
- Functions f(x) = cases x - 1, & x < 2 2x - 3, & x 2 cases is continuous
- The value of p for which the function f(x) = cases (4^x - 1)^3 ( x p ) (1 + x^2 3 ) , & x 0 [2mm] (12)( 4)^3, & x = 0 cases may...
- If f(x) = cases x^a 1 x , & x 0 0, & x = 0 cases is continuous at x = 0, then
- If f(x) = cases x^2 4 - 3x 2 + 13 4 , & x < 1 [1mm] |x - 3|, & x 1 cases , then f(x) is
- If f(x) = (x^2 - x) x for x 0 is continuous at x = 0, then f(0) is
- If f(x) = cases x^2 + 3x + k 2(x^2 - 1) , & x 1 [1mm] 5 4 , & x = 1 cases is continuous at x = 1, then
- If f(x) = x - a x - a is continuous at x = a, then f(a) is equal to
- If the function f(x) = ^2 x - ^2 x - 1 x^2 + 1 - 1 is continuous at x = 0, then f(0) is equal to
- If the function f(x) = cases x^2 - (A + 2)x + A x - 2 , & for x 2 [1mm] 2, & for x = 2 cases is continuous at x = 2, then
- If f(x) = cases (1 + 4x 5 )^ 1 x , & x 0 [1mm] e^ 4 5 , & x = 0 cases then correct statement is:
- If f(x) = cases ^ -1 |x|, & when x 0 0, & when x = 0 cases , then
- Which of the following functions is continuous at x = 0?
- Let f(x) = cases x 5x , & x 0 k, & x = 0 cases . If f(x) is continuous at x = 0, then k =
- If f(x) = cases x e^ 1/x + 1 , & when x 0 0, & when x = 0 cases , then
- f(x) = cases 2x + 1, & x < 1 2, & x = 1 x^2 + 1, & x > 1 cases is:
- If f(x) = cases x^6 - 1 64 x^3 - 1 8 , & x 1 2 [1mm] k, & x = 1 2 cases is continuous at x = 1 2 , then the value of k is
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