show-that-tan-xx-for-0-xpi-2-hint-show-that-fxtan-x-x-is-increasing-on-0-pi-2

Question

Show that $	an x>x$ for $0< x<\pi / 2 .[$Hint : Show that $f(x)=	an x-x$ is increasing on $(0, \pi / 2) . ]$

Jack Chen · Accepted Answer

the next question when we want to show that in your next is greater the next time interval. So first, um, we defined a function if equals Teoh 10 gen x minus six and the ways we can see that if if, if x equals zero f of zero cost zero because 10 gen x 10 Jan 00 Um, so we take the first I wanna do with your life We have can square X minus one Um, so maybe you can write in, ah one over co sign off X square minus one the only interval from zero Too high half because he costs i off x is strictly less No. One. And that means call sign X Square is strictly lesson one and later tells us one or a close eye. X squared is strictly great in a one and them use the first of the curative off. If it&#x27;s strictly, Lesson zero is strictly greater than zero. And that means if is increasing. So if f is increasing and we know F zero equals zero. So if off X were greater than a 40 here o x in the interval from zero to pi half That means if off X is greater than zero, which means 10 gen x minus X Griffin&#x27;s your oh so tender excuse great and pecs and they were finished approach here.

Carson Merrill · Answer

taking the tangent of X minus X. We see that it&#x27;s increasing. I&#x27;m on the interval from zero to pi over two. What this shows us is that another way you could do Look at this is if we take the derivative function we see that this is always positive and increasing, so that ultimately tells us that the function tangent of X is going to be greater than the function just X.

Helen Latting · Answer

so the equation were supposed to prove is that the absolute value of X is the cynical to the tin gypped X where at the value of X Is that some pie too? So the first thing we&#x27;re gonna dio is we&#x27;re gonna right Tension of X as tangent X minus Attention, zero because tension of 00 then we divide both sides by X minus zero and then here this looks like the mean value. The&#x27;re, um some because that that equal to the derivative of tension of X um, which is secret Squared X, see, considered X. Um, And then you multiply both sides by ex Um, we&#x27;re gonna rewrite this as huh Um, Tangent ex tension of zero equals zero equals X times seek it squared X um, and then you can take absolute value off both sides. And then that proves that, um, X is gonna be less than or kill to absolute value of X. Just unequal to tangent of X. On the interval, X is less than hi over to

Ankit Gupta · Answer

we have to prove that Don inverse off X plus Don and worse off. One divided by X is equal toe hydrated by two effects is greater than zero. So let via one the equal toe down in verse. Affix. That means Don why one is equal to X. Let vital be equal toe done and worse off. One divided by X, which means gone off vital will be equal toe one divided by X now, since via one plus y, two will be equal to fight invaded by two. So putting the values we can write that Dunnan voice affects plus Don inverse off one divided by X will be equal to fight abated by two, hence approved.

Leon Druch · Answer

in this problem, we want to show that sine of X is less than X on the interval. Uh Where zero is less than X, which in turn is less than two pi. So X is in this interval from zero, not including zero up to two pi, not including two pi. So on this interval where X is between zero and two pi, we want to show that sine of X is less than X. If sine of X is less than X, that means X is greater than sign of X. And if X is greater than sign of X then x minus sine of X would have to be greater than zero. So we can show that X is greater than sign of X on this interval. Uh huh. We can show that X is greater than sign of X on this interval between zero and two pi. Uh If we can show that X minus sine of X is positive on this interval between zero and two pi remember we&#x27;re not including zero because at the point X equals zero X and sine of X um are equal to each other. Uh But for X values greater than zero and less than two pi, you can see graphically uh that the function x minus sine of X is a positive function because it&#x27;s graph stays above the X axis. So X minus sine of X is positive, which means X must be larger or greater than sign effects

Michelle Ling · Answer

So we want to prove that X is less than or equal to tangent so we can set after backed ableto acts and G rex equal to 10 gin packs. So if we, um and also this is over the interval 02 pi over to so they play an X equals zero. For both of these functions, we see that after zero Andrea zero, both equal zero so vexed can equal jia backs. Now we want to find the derivative of both of these functions. So here we can use the power down roll on for she prime of X. We can use our trigger als um and so here we know that the derivative of af of axes last then or equal to you derivative of Jeeva over over this interval here. And since we have this statement, you have this statement and we have this statement. According to the previous exercise, we can conclude that F of X is less than or equal to g of AKs and thus if we replace you functions, we can conclude that axe is less than or equal to tension. X for ex being

Problem

(a) Show that $e^{x} \geqslant 1+x$ for $x \geqsl…

Problem 57 Hard Difficulty

Show that $\tan x>x$ for $0< x<\pi / 2 .[$Hint : Show that $f(x)=\tan x-x$ is increasing on $(0, \pi / 2) . ]$

Answer

$\tan x>x$ for $x \in\left(0, \frac{\pi}{2}\right)$

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$\tan x>x$ for $x \in\left(0, \frac{\pi}{2}\right)$

Essential Calculus Early Transcendentals

Grace H.

Catherine R.

Anna Marie V.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartEssential Calculus Early Transcendentals

Grace H.

Catherine R.

Anna Marie V.

Joseph L.

James Stewart

Essential Calculus Early Transcendentals