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.
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