Give an example of a nowhere continuous function fx where fx

Give an example of a nowhere continuous function f(x) where |f(x)| is continuous everywhere. Give an example of a function f(x) which is continuous everywhere, but it is not differentiable everywhere. Give an example of a function fix) which is continuous at only one point. Find all values of k that will make the following function continuous everywhere. F(x) = {(2x^2 - x - 15)/(x - 3), if x notequalto 3 kx - 1 if x = 3 Use Taylor\'s Polynomial to derive Newton\'s Formula. Is there a root between 0 and 1 for the polynomial f(x) = 4x^3 - x^2 + 7x - 5? Justify your answer. Use Newton\'s Formula to find a real solution. Let X (a, b, c, d, e). Determine whether or not each of the following clauses of subsets of X is a topology on X. Prove that a finite set does not have any limit (cluster or accumulation) points. Give the value of the following unions or intersections.

Solution

10)

Here for no where continuous function but |f(x)| to be continuous we can choose:

f(x)= 1 when x belongs to rational numbers

f(x)=-1 when x belongs to R\\Q