Prove that the identity function on real numbers given by f(x)= x is continuous at every real number.

Prove that the function defined by f(x)= tan x is a continuous function.

Is the function defined by f(x)= |x| , a continuous function?

Prove that every rational function is continuous.

Prove that the function f(x)= 5x-3 is continuous at x=0, at x= -3" and at " x=5 .

Discuss the continuity of the function f given by f(x)= |x|" at "x=0 .

Let f(x) be an even function forall x in R If f(x) is continuous at x = a, prove that it is continuous at x = - a.

Restate the following statements with appropriate conditioins, so that they become true statements. i. For every real number x, 3x gt x . ii. For every real number x, x^(2) ge x iii. If you divide a number by two, you will always get half of that number. iv. The angle subtended by a chord of a circle at a point on the circle is 90°. v. If a quadrilateral has all its sides equal, then it is a square.

Let f (x) be an odd function for continuous at x in R If f(x) is continuous at x = a, prove that it is continous at x=-a

Check whether the following pair of statements are negation of each other. Give reasons for your answer x + y = y + x is true for every real numbers x and y. There exists real numbers x and y for which x + y = y + x.

Show that the function f defined by f(x)= |1-x+|x|| , where x is any real number, is a continuous function.