Prove that the function `f` given by `f(x)=x-[x]` is increasing in `(0,\ 1)` .

Prove that the function f given by f(x)=x-[x] us increasing in (0,1)dot

Let I be any interval disjoint from (1, 1) . Prove that the function f given by f(x)=x+1/x is strictly increasing on 1.

Prove that the function f given by f(x) = log sin x" is increasing on "(0,pi/2) and decreasing on (pi/2,pi) .

Show that the function f given by f(x)=10^x is increasing for all x .

Prove that the function f given by f(x) = log | cos x|" is decreasing on "(0,pi/2)" and increasing on "((3pi)/2,2pi) .

Prove that the function f given by f(x)=logcosx is strictly increasing on (-pi//2,\ 0) and strictly decreasing on (0,\ pi//2) .

Prove that the function f given by f (x) = log cos x is strictly decreasing on (0,pi/2) and strictly increasing on (pi/2,pi) prove that the function f given by f(x) = log sin x is strictly decreasing on ( 0 , pi/2) and strictly increasing on ( pi/2 , pi) ..

Prove that the function f defined by f(x)=x^2−x+1 is neither increasing nor decreasing in (−1,1) . Hence find the intervals in which f(x) is strictly increasing and strictly decreasing.

Find the least value of a such that the function f given by f(x)=x^2+a x+1 is strictly increasing on (1, 2)dot

Prove that the function f(x)=(log)_e x is increasing on (0,\ oo) .