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WebIf X is infinite-dimensional, to show the existence of a linear functional which is not continuous then amounts to constructing f which is not bounded. ... Define an operator T which takes the polynomial function x ↦ p(x) on [0,1] to the same function on [2,3]. As a consequence of the Stone–Weierstrass theorem, ... Web29 Mar 2024 · If f (x) = x 2 sin 1/x, where x ≠ 0, then the value of the function f at x = 0, so that the function is continuous at x = 0 , is (A) 0 (B) – 1 (C) 1 (D) none of these This … demon slaying chronicles manhwa
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WebShow that the function f (x) = { x 2 sin x 1 , x 6 = 0 0 , x = 0 is differentiable at all x ∈ IR. Also show that the function f ′(x) is not continuous at x = 0. Thus, a function that is differentiable at every point of IR need not have a continuous derivative f ′(x). Show that the function f (x) = WebThe probability mass function (pmf) specifies the probability distribution for the sum of counts from two dice. For example, the figure shows that . The pmf allows the computation of probabilities of events such as , and all other probabilities in the distribution. WebIf f(x)={xsin x1,x =0k , x=0} is continuous at x=0, then the value of k is A 1 B −1 C 0 D 2 Easy Solution Verified by Toppr Correct option is C) If function f(x) is continuous at x=0, then … ff5870