Show that in the limit ?x ? 0 ?y ? 0 ?r ? 0 the difference is equivalent to the two-dimensional version of the differential

GIVEN
Difference equation,
SHOW
(a) In the limit ?x , ?y, and ?r ? 0 the difference equation is equivalent to the two-dimensional
version of the differential equation,




We have by definition



is equivalent to



so the difference equation becomes



which is equivalent to the two-dimensional version as required.

Physics & Space Science

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