Show that sinx is continuous for every real x.

Show that : sin^2x is continuous for everyreal value of x.

Answer all questions (j) A function f(x) is defined as f(x) = {{:((x^2 - x - 6)/( x-3)",","if" xne 3),(5",","if"x=3):} Show that f(x) is continuous at x=3 .

Show that f(x)=|x| is continuous at x=0 but not deferentiable at x=0 .

Examine that sin|x| is a continuous function.

Show that tangent function is continuous in their domain

Identify the quantifiers of the following statements For every real number x, x^2 != x

If f(x)=|x|^(3) , then show that f''(x) exists for all real x and find it.

Show that the function f(x)=|x-3|,x in R is continuous but not differentiable at x=3

By giving counter examples , show that for every real number x and y, x^2=y^2 implies x =y are not true:

Show that the function f(x)=2x-|x| is continuous at x=0 .