Define the continuity of `f(x)" at " x= a` . When is the function said to be continuous in the closed interval `alexleb` ?

State when the function f(x) is said to be decreasing in a finite interval a le x le b .

State when the function f(x) is said to be increasing in a finite interval a le x le b .

The function f (x) is continuous at x = 0 of -

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

Prove that the function f (x) = 5 is continuous at x = 2 .

The function f(x)=x^(k) is continuous at x = k when -

Show that the function f(x)=x|x| is continuous and differentiable at x = 0

Show that the function f(x)=|sinx+cosx| is continuous at x = pi .

Define the continuity of a function at a point within its domain of definition. The definition of a function is given below: f(x)={{:((1-cos5x)/(x^(2))," when "(xne0)),(k," when x = 0"):} Find the value of k for which f(x) is continuous at x = 0.

Discuss the continuity of the following functions : f(x)= sin x +cos x