Explore BrainMass

Explore BrainMass

    Real analysis

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    29.12 (a) Show that x < tan x for all x in (0, &#960;/2).

    (b) Show that x/ sin x is strictly increasing function on (0, &#960;/2).

    (c) Show that x &#8804; (&#960;/2)&#1468;sin x for all x in [0, &#960;/2].

    © BrainMass Inc. brainmass.com December 24, 2021, 5:09 pm ad1c9bdddf


    Solution Preview

    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 ...

    Solution Summary

    There are three proofs here involving trigonometric functions.