Question

show that x/1+x² less than tan*-1 x less than x when x greater than 0​

Answer 1

Answer:

Step-by-step explanation:

Consider a function f(x)=ln(x+1)−x/x+1.

So basically we need to prove that f(x) > 0∀x > 0.

f′(x)=1/x+1−1/(x+1)^2

    =x/(x+1)^2 > 0∀x >0

Thus f(x) is a strongly increasing function.

As f(0)=0

⇒f(x) > 0∀x > 0