Chapter 1: Limits
Section 1.1: Naive Limits
Control-drag (or type) fx=…
Context Panel: Assign Function
fx=sin1/x→assign as functionf
Figure 1.1.7 shows the oscillatory behavior of f. As x nears zero, 1/x becomes larger and larger. Hence, all the oscillations of sinθ for larger and larger values of θ are compressed into the region near x=0. Consequently, fx assumes all the values of sinθ repeatedly, and the limit will fail to exist because of "infinite oscillation."
Figure 1.1.7 Graph of fx=sin1/x
Expression palette: Limit template
Context Panel: Evaluate and Display Inline
limx→0fx = −1..1
Maple indicates that the limit fails to exist by returning a range from -1 to 1. This indicates that the function takes on all values between -1 and 1, and takes them on infinitely often. A typical calculus text would not use this notation, but would simply say that the limit fails to exist because of infinite oscillation.
<< Previous Example Section 1.1
Next Example >>
© Maplesoft, a division of Waterloo Maple Inc., 2023. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.
For more information on Maplesoft products and services, visit www.maplesoft.com
Download Help Document