When are graphs deceiving? What are some examples of functions or quantities relating to functions (e.g., limits) $f:A \to B$ where $A$, $B \subseteq \mathbb{R}$ that require by-hand, "analytical" methods for analysis which are seemingly contradicted by a graph generated by software?
For instance, I recall that a Pre-calculus text stated that $\lim\limits_{x \to 0}\dfrac{1-\cos x^{6}}{x^{12}} = \dfrac{1}{2}$ (which, if I recall correctly, is proven using Taylor series) but the graph itself seems to suggest that it perhaps doesn't exist, due to the oscillations occurring around 0. [Graphs were generated via WolframAlpha.]



A classical example is $$\lim_{x \to 0} x^2 \sin\left(\frac{1}{x}\right)$$
