Sketch the graphs of the curves y = 1 x2, y = cos x,and y = f(x), where f is a function

Chapter 1, Problem 64

(choose chapter or problem)

Sketch the graphs of the curves \(y=1-x^{2}\), \(y=\cos x\), and \(y = f(x)\), where \(f\) is a function that satisfies the inequalities

\(1-x^{2} \leq f(x) \leq \cos x\)

for all x in the interval \((-\pi / 2, \pi / 2)\). What can you say about the limit of \(f(x) \text { as } x \rightarrow 0\)? Explain.

Equation Transcription:

y = 1 − x2

y = cos x

y = f(x)

f

1 - x2  f(x)  cos x

(−/2, /2)

f(x) as x→0

Text Transcription:

y = 1 − x^2

y = cos x

y = f(x)

f

1 - x^2 leq f(x) leq cos x

(−pi/2, pi/2)

f(x) as x right arrow 0