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

1 Answer
May 13, 2018

Answer:

See below

Explanation:

#y=xcos(1/x)#

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

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

The limit of #y# as #x->0 = 0#.

We can see these features from the graphs of #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]}