Continuity and Differentiability questions
732 published questions with worked solutions.
- The function f(x) = cases ^3( x ) (1 + 3x) ( ^ -1 x )^2(e^ 5 x - 1)x , & x 0 [2mm] a, & x = 0 cases is continuous at [0, 1], if
- The function f(x) = [x]^2 - [x^2], (where [y] is the greatest integer less than or equal to y), is discontinuous at
- Let f(x) = cases x^3 + x^2 - 16x + 20 (x - 2)^2 , & if x 2 [2mm] k, & if x = 2 cases . If f(x) be continuous for all x, then k =
- The function f(x) = |x| is
- The function f(x) = (x - 1)^ 1 (2 - x) is not defined at x = 2. The value of f(2) so that f is continuous at x = 2 is
- The function f(x) = cases x + 2, & 1 x 2 4, & x = 2 3x - 2, & x > 2 cases is continuous at
- If the function f(x) = cases 1 + x 2 , & for - < x 1 ax + b, & for 1 < x < 3 6 x 12 , & for 3 x < 6 cases is continuous in the...
- The value of f(0), so that the function f(x) = a^2 - ax + x^2 - a^2 + ax + x^2 a + x - a - x becomes continuous for all x, is...
- If f(x) is continuous over [- , ], where f(x) is defined as f(x) = cases -2 x, & - x - 2 x + , & - 2 < x < 2 x, & 2 < x cases...
- The value of f(0), so that the function f(x) = 1 - (1 - x) x^4 is continuous everywhere, is
- If f(x) = cases 1, & when 0 < x 3 4 2 2 9 x, & when 3 4 < x < cases , then
- For every integer n, let a_n and b_n be real numbers. Let function f : R R be given by f(x) = cases a_n + x & for x [2n, 2n + 1]...
- Let f(x) = 1 - x 4x - , x 4 , x [0, 2 ]. If f(x) is continuous in [0, 2 ], then f ( 4 ) is
- In the function f(x) = 2x - ^ -1 x 2x + ^ -1 x , (x 0) is continuous at each point of its domain, then the value of f(0) is
- The values of a and b such that the function defined by f(x) = cases 7, & if x 2 ax + b, & if 2 < x < 9 21, & if x 9 cases is a...
- If f(x) = |x - b|, then function
- If function f(x) = cases x, & if x is rational 1 - x, & if x irrational cases then f(x) is continuous at ......... number of...
- Let f(x) = cases (1 + | x|)^ a | x| , & - 6 < x < 0 b, & x = 0 e^ 2x 3x , & 0 < x < 6 cases Then the values of a and b if f is...
- If f(x) = 10^x + 7^x - 14^x - 5^x 1 - x , for x 0 = 10 7 , for x = 0, then f(x) is
- If the function f(x) = cases 5x - 4, & if 0 < x 1 4x^2 + 3bx, & if 1 < x < 2 cases is continuous at every point of its domain,...
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