Chapter 1: Limits
Section 1.1: Naive Limits
Evaluate limx→0x sin1/x.
Control-drag (or type) fx=…
Context Panel: Assign Function
fx=x sin1/x→assign as functionf
Figure 1.1.8(a) shows the oscillatory behavior of f. However, because of the multiplicative factor x, the oscillations shown in Figure 1.1.7 are encased by between the lines y=±x. As x approaches zero, these oscillations are squeezed to zero, and the limit now exists and is, in fact, zero.
Figure 1.1.8(a) Graph of fx=x sin1/x
Expression palette: Limit template
Context Panel: Evaluate and Display Inline
limx→0fx = 0
Maple's limit operator correctly applies Principle 1.1.1 and determines the value of the limit to be zero.
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