a) Using a graphing calculator, show that if 0 < x < 1, then x ––< sin x < x. Sketch the three functions over the interval [0, 1]. b) Similarly, using a graphing calculator, show that if –1 < x < 0, then x –=> sin x 2 x. Add these portions of the three graphs to the graph in (a). c) Explain why sin x S1 for –1 < x < 1, x # 0. Hint: use the inequalities in (a) and (b) to help you.
a) Using a graphing calculator, show that if 0 < x < 1, then x ––< sin x < x. Sketch the three functions over the interval [0, 1]. b) Similarly, using a graphing calculator, show that if –1 < x < 0, then x –=> sin x 2 x. Add these portions of the three graphs to the graph in (a). c) Explain why sin x S1 for –1 < x < 1, x # 0. Hint: use the inequalities in (a) and (b) to help you.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 25T
Related questions
Question
Transcribed Image Text:sin x
d) Using answers in (a) and (b), find a function f (x) with f (x) <
on –1< x < 1,
x + 0, such that lim f (x) = 1.
sin x
e) Using parts (c) and (d), compute lim
x-0 x
![x3
a) Using a graphing calculator, show that if 0 <x< 1, then x -:
< sin x < x. Sketch
the three functions over the interval [0, 1].
b) Similarly, using a graphing calculator, show that if –1 < x < 0, then x –
sin x > x. Add these portions of the three graphs to the graph in (a).
sin x
c) Explain why
< 1 for –1<x< 1, x # 0. Hint: use the inequalities in (a) and (b)
to help you.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb070bf01-5e91-4c2b-bb3b-adde043c5b6f%2F1f00ea71-a743-4e51-bef1-735593b141e8%2F9lk1r5t_processed.png&w=3840&q=75)
Transcribed Image Text:x3
a) Using a graphing calculator, show that if 0 <x< 1, then x -:
< sin x < x. Sketch
the three functions over the interval [0, 1].
b) Similarly, using a graphing calculator, show that if –1 < x < 0, then x –
sin x > x. Add these portions of the three graphs to the graph in (a).
sin x
c) Explain why
< 1 for –1<x< 1, x # 0. Hint: use the inequalities in (a) and (b)
to help you.
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