How do you find the graph of $y = x cos (\frac{1}{x})$ $y=xcos(1/x)$ ?

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Answer 1 · 2018-05-13T13:08:56

See below

$y = x cos (\frac{1}{x})$ $y=xcos(1/x)$

For large $x$ $x$ , $y \to x$ $y -> x$ so for large $x$ $x$ the graph tends to $y = x$ $y=x$

However, as $x$ $x$ approaches 0 from below and above the graph oscillates with ever greater frequency and diminishing amplitude.

The limit of $y$ $y$ as $x \to 0 = 0$ $x->0 = 0$ .

We can see these features from the graphs of $y$ $y$ below.

graph{xcos(1/x) [-0.6537, 0.6786, -0.327, 0.339]}

graph{xcos(1/x) [-28.85, 28.86, -14.43, 14.45]}

How do you find the graph of y=xcos(1x)y=xcos(1/x)?