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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?.
Where
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
is continuous?
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 – s^{2}>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
RHL:
LHL:
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) = [(x^{2})^{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, ∞]?
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