Prove that cot x is continuous in its domain

Prove that tangent function is continous in its domain.

Let function f be defined as f:R^(+)toR^(+) and function g is defined as g:R^(+)toR^(+) . Functions f and g are continuous in their domain. Suppose, the function h(x)=lim_(ntooo)(x^(n)f(x)+x^(2))/(x^(n)+g(x)), x gt0 . If h(x) is continuous in its domain,then f(1).g(1) is equal to (a) 2 (b) 1 (c) 1/2 (d) 0

Statement -1 : y = [x] , ([.] denotes greatest integer function) is not a continuous function . Statement -2 : {x} ({.} denotes fractional fractional function) is discontinuous at integral points. Statement -3 : y = 7^(x) is continuous in its domain.

If f(x)=|(log)_e|x|| , then (a) f(x) is continuous and differentiable for all x in its domain] (b) f(x) is continuous for all x in its domain but not differentiable at x=+-1 (c) f(x) is neither continuous nor differentiable at x=+-1 (d) none of these

If f is continuous on its domain D; then |f| is also continuous on D

If f is continuous on its domain D; then |f| is also continuous on D

If f is continuous on its domain D; then |f| is also continuous on D

Prove that f(x)=sqrt(|x|-x) is continuous for all xgeq0.

Prove that f(x)=sqrt(|x|-x) is continuous for all xgeq0 .

Prove that: cot2A + tanA= cotA - cot 2A