Give an example of a function f which satisfies the initial value problemI.V.P on a closed and bounded interval [a, b], but is not continuous on [a, b]

Give an example of a function that is uniformly continuous on R but is not bounded on R.

consider the interval (0,1] element of R. show that there exist a continuous function f:(0,1] to R is not bounded on (0,1] construct a construct continuous function f:[0, inf) to R which is not bounded . what has got these examples to do with compactness of the domain

Give an example of a continuous preference relation anda discontinuous utility function that represents the preference relation.

Let f be a function such that f (1) = − 2 and f (5) = 7. Which of the following conditions ensures that f(c) = 0 for some value c in the open interval (1,5)?Responses∫15𝑓(𝑥)𝑑𝑥 exists. Integration of f of x of d x exists from 1 to 5f is increasing on the closed interval [1, 5].f is increasing on the closed interval [1, 5].f is continuous on the closed interval [1, 5].f is continuous on the closed interval [1, 5].f is defined for all values of x in the closed interval [1, 5].

Which of the following functions is continuous for every value of x except x=0?