29.12 (a) Show that x < tan x for all x in (0, π/2).
(b) Show that x/ sin x is strictly increasing function on (0, π/2).
(c) Show that x ≤ (π/2)ּsin x for all x in [0, π/2].© BrainMass Inc. brainmass.com December 24, 2021, 5:09 pm ad1c9bdddf
Please see the attachment.
We need to following theorems for the questions.
Theorem 1: Suppose the function is differentiable on the interval . If for all , then is strictly increasing on . If for all , then is strictly decreasing on . If for all , then is increasing on . If for all , then is decreasing on .
Theorem 2 (Quotient Rule): Suppose the functions ...
There are three proofs here involving trigonometric functions.