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

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

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 3

Derivatives and the Shapes of Graphs

Derivatives

Differentiation

Applications of the Derivative

Missouri State University

Campbell University

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

00:28

If $f$ is increasing on an…

01:45

Prove that $|x| \leq|\tan …

00:55

Prove that if $x>0, \ta…

0:00

Show that $ \sin x < x …

01:24

Use Exercise 67 to prove t…

01:33

Show that $\tan (x / 2)$ h…

02:34

$$\text { Solve: } \qu…

02:00

Solve for $x$ in the indic…

03:08

01:31

Prove the identity.$$\…

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'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's your oh so tender excuse great and pecs and they were finished approach here.

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In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

If $f$ is increasing on an interval $[0, b),$ then it follows from Definitio…

Prove that $|x| \leq|\tan x|$ for $|x|<\frac{\pi}{2}.$

Prove that if $x>0, \tan ^{-1} x+\tan ^{-1} \frac{1}{x}=\frac{\pi}{2}$.

Show that $ \sin x < x $ if $ 0 < x < 2\pi $.

Use Exercise 67 to prove that $x \leq \tan x$ for $0 \leq x<\frac{\pi}{2}…

Show that $\tan (x / 2)$ has the same sign as $\sin x$ for any real number $…

$$\text { Solve: } \quad \tan ^{2} x-\sec x-1=0,0 \leq x<2 \pi$$<…

Solve for $x$ in the indicated interval.$$2 \tan ^{2} x-3 \tan x+1=0,0 \…

Solve for $x$ in the indicated interval.$$\tan 2 x+3 \tan x=0,0<x \le…

Prove the identity.$$\tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}$$

00:54

Solve each equation for $x$$$\text { (a) }\ln (\ln x)=1 \quad \text …

04:56

Use the methods of this section to sketch the curve $y=x^{3}-3 a^{2} x+2 a^{…

02:46

Show that the curves $y=e^{-x}$ and $y=-e^{-x}$ touch the curve $y=e^{-x} \s…

00:40

$15-18=$ Express the limit as a definite integral on the giveninterval.<…

00:59

Evaluate the limit, if it exists.$$\lim _{x \rightarrow 5} \frac{x^{2}-5…

08:08

$19-23$ . Use the form of the definition of the integral given inTheorem…

02:03

Evaluate the integral using integration by parts with theindicated choic…

00:22

Find the limit.$$\lim _{x \rightarrow 2} \log _{5}\left(8 x-x^{4}\ri…

11:39

The frame for a kite is to be made from six pieces of wood.The four exte…

03:01

$1-30=$ Evaluate the integral.$$\int_{-2}^{3}\left(x^{2}-3\right) d x$$<…

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