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A saltus at point of continuity is equal to
Which of the following functions f: Z X Z → Z is not onto?
The function is not onto as f(a) ≠ b.
Assertion (A) : If is continuous on [a ,b] then there exists a real number u such that f(x) ≤ u,
Reason (R) : If is continuous in [a,b] then it attains its bounds in [a, b].
Let f be defined for all real x such that |f(x) - f(y)| < (x - y)2 for all real x and y, then
What is the domain and range of f?.
Here, function is defined in stages, for x ≥ 1: the formula y = x is defined for all values of x greater than or equal to unity. The domain for this part is [1, ∞].
For x < 1 is defined for all values less than unity. Then the domain of this part is (– ∞ ,1).
Hence, domain of given function is (– ∞ ,1) ∪ [1, ∞) = (– ∞, ∞).
For what value of k, the function
For function f(x,y) to have minimum value at (a,b) value is?
For the function f(x,y) to have minimum value at (a,b)
rt – s2>0 and r>0
where, r = ∂2f⁄∂x2, t=∂2f⁄∂y2, s=∂2f⁄∂x∂y, at (x,y) => (a,b)
If f (x) = then which of the following is incorrect?
An example of a function on the real line R i.e., continuous but not uniformly continuous is
Let f: [0, 10] → [0, 10] be a continuous mapping, then
For the function f (x) defined as
So, the function is not continuous at the point x = 2 and having an infinite discontinuity of the second kind.
Under which one of the following conditions does the function f(x) = [(x2)m sin (x-2)n], x ≠ 0, n > 0 and f(0) = 0, have a derivative at x = 0?
Suppose f: [a, b] → R is continuous on [a, b] and f is differentiable on (a, b). If f(a) = f(b), there is c ∈ (a,b)-.f'(c) = 0
Let y be continuously differentiable function which satisfies the differential equation
y" + y' - y = 0,
where a is a positive real number, if y(0) = y(a) - 0, then on [0, a].
If f(x) = then which of the following is incorrect?
If f is decreasing function on E ⊂ R, then for x, y ∈ E, We have
Which one is uniformly continuous in [0, ∞]?