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Argue that $\sin x$ is an increasing function on $0 \leq x \leq \pi / 2$.

Calculus 1 / AB

Chapter 8

Applications of Derivatives

Section 1

Some geometry of the derivative

Differentiation

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

44:57

In mathematics, a differen…

01:54

01:07

State whether the function…

01:57

01:18

0:00

Show that $ \sin x < x …

By inspecting a graph of $…

01:41

00:58

01:04

00:53

Simplify $\sin ^{-1}(\sin …

00:43

01:58

Show that $\tan x>x$ fo…

01:25

Show that $ \tan x > x …

00:54

01:26

Determine whether the stat…

01:19

$y=\sin ^{-1} x$ means…

03:18

CHALLENGE Present a logica…

01:36

Prove that $$0 \leq \int_{…

01:40

Is the graph of the functi…

uh, we are quiet too. Deter Mined within the end of all off by negative by over two. And try over to to check whether the graph is increasing or decreasing. Now negative by over two is here on the dead drum and then pi over two. He is also here. Yes. So we didn't is in Deval. It is clear that our graph is going Graph is increasing. Therefore we can see function that is inclusive.

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In mathematics, a differentiation rule is a rule for computing the derivativ…

State whether the function $y=\sin x$ is increasing or decreasing on the giv…

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

By inspecting a graph of $y=\sin x$ or $y=\cos x,$ determine whether the fun…

Simplify $\sin ^{-1}(\sin x)$ if $-\pi / 2 \leq x \leq \pi / 2$.

State whether the function $y=\cos x$ is increasing or decreasing on the giv…

Show that $\tan x>x$ for $0< x<\pi / 2 .[$Hint : Show that $f(x)=\t…

Show that $ \tan x > x $ for $ 0 < x < \pi /2 $. [Hint: Show that $…

Determine whether the statement is true or false. Justify your answer.$$…

$y=\sin ^{-1} x$ meanswhere $-1 \leq x \leq 1$ and $-\frac{\pi}{2} \leq …

CHALLENGE Present a logical argument for why the identity $\sin ^{-1} x+\cos…

Prove that $$0 \leq \int_{\pi / 4}^{\pi / 2} \frac{\sin x}{x} d x \leq \frac…

Is the graph of the function $y=\sin x$ increasing or decreasing over the in…