At the beginning of this section we considered the function f ( x , y ) = sin ( x 2 + y 2 ) x 2 + y 2 and guessed on the basis of numerical evidence that f ( x , y ) → 1 as ( x , y ) → (0, 0). Use polar coordinates to confirm the value of the limit. Then graph the function.
At the beginning of this section we considered the function f ( x , y ) = sin ( x 2 + y 2 ) x 2 + y 2 and guessed on the basis of numerical evidence that f ( x , y ) → 1 as ( x , y ) → (0, 0). Use polar coordinates to confirm the value of the limit. Then graph the function.
Solution Summary: The author explains that the limit of the function f(x,y)=mathrmsin left is 1 using polar coordinates and sketch the graph.
At the beginning of this section we considered the function
f
(
x
,
y
)
=
sin
(
x
2
+
y
2
)
x
2
+
y
2
and guessed on the basis of numerical evidence that f(x, y) → 1 as (x, y) → (0, 0). Use polar coordinates to confirm the value of the limit. Then graph the function.
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