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How do you graph #r=2+4costheta# on a graphing utility?

Answer 1

Emery Adkins

See the limacon details and graph.

#cos theta in [ - 1, 1 ]#

0<= r = 2 + 4 cos theta in [ 2 - 4, 2 + 4 ]#

#= [ 0, 6 ],# sans negative, and so,

no plotting, for #theta in [ 2/3pi, 4/3pi ]#, in #theta#- positive,

anticlockwise measurement..

Period of r = period of # cos theta = 2pi#.

Multiply both sides by r and use

# cos theta = x/r and r = sqrt ( x^2 + y^2 )#

Now, the Cartesian form for Socratic graphic utility is obtained.

#x^2 + y^2 = 2sqrt ( x^2 + y^2 ) + 4x#. The dimpled apple-like

graph is immediate.

graph{ x^2 + y^2 - 2sqrt ( x^2 + y^2 ) - 4x=0 [ - 6 10 -4 4 ]}

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.