Use the Squeezing Theorem to show thatlimx0x cos 50x = 0and illustrate the principle

Chapter 1, Problem 61

(choose chapter or problem)

Use the Squeezing Theorem to show that

\(\lim \limits_{x \rightarrow 0} x \cos \frac{50 \pi}{x}=0\)

and illustrate the principle involved by using a graphing utility to graph the equations \(y=|x|\), \(y=-|x|\), and \(y=x \cos (50 \pi / x)\) on the same screen in the window [−1, 1] × [−1, 1].

Equation Transcription:

 x cos  = 0

y = | x |

y = - | x |

y = x cos (50/x)

Text Transcription:

lim_x right arrow 0 x cos 50pi/x = 0

y = |0|

y = - |x|

y = x cos (50pi/x)