Continuity and Differentiability questions
732 published questions with worked solutions.
- Let a function f : R R, where R is the set of real nos. satisfying the equation f(x + y) = f(x) + f(y) x, y if f(x) is continuous...
- f(x) = x + |x| is continuous for
- The function f(x) = 3x + 3 is continuous in
- If the function f(x) = 6x 3x , x 0 is continuous at x = 0, then f(0) is equal to
- If f(x) = x + 3 - 2 x^3 - 1 , x 1 is continuous at x = 1, then f(1) is equal to
- If f(x) = x - 7 x^2 - 49 is continuous at x = 7, then f(7) is
- If f(x) = 3^x + 3^ -x - 2 x^2 for x 0 is continuous at x = 0, if f(0) is equal to
- If f(x) = cases x^6 - 1 64 x^3 - 1 8 , & x 1 2 [2mm] k, & x = 1 2 cases is continuous at x = 1 2 , then the value of k is
- If f(x) = cases x - 3 x - 3 , & x 3 [1mm] c, & x = 3 cases is continuous at x = 3, then the value of c is
- f(x) = x + |x| is continuous for
- If function f(x) = cases x, & if x is rational 1 - x, & if x is irrational cases , then the number of points at which f(x) is...
- Let f(x) = cases 5^ 1/x , & x < 0 [x], & x 0 cases and R, then at x = 0
- The value of f(0) so that f(x) = (-e^x + 2^x) x may be continuous at x = 0 is
- Let f(x) = 1 - x 4x - , x 4 , x [0, 2 ]. If f(x) is continuous in [0, 2 ], then f ( 4 ) is equal to
- The function f : R/ 0 R given by f(x) = 1 x - 2 e^ 2x - 1 can be made continuous at x = 0 by defining f(0) as
- Function f(x) = cases x - 1, & x < 2 2x - 3, & x 2 cases is a continuous function
- For the function f(x) = cases x^3 - a^3 x - a , & x a b, & x = a cases if f(x) is continuous at x = a, then b is equal to
- If the function f : R R given by f(x) = cases x + a, & if x 1 3 - x^2, & if x > 1 cases is continuous at x = 1 then a is equal to
- Let f(x) = (e^x - 1)^2 ( x a ) (1 + x 4 ) for x 0 and f(0) = 12. If f is continuous at x = 0, then the value of a is equal to
- If f(x) = cases mx + 1, & x 2 x + n, & x > 2 cases is continuous at x = 2 , then
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