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Find the limit, if it exists, of lim (x, y) → (0, 0) x⁴ - 40y² / (x² + 20y²)?

User OriEng
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Final answer:

To find the limit of the expression, substitute x = 0 and y = 0 into the expression and simplify.

Step-by-step explanation:

To find the limit of the expression, we can substitute the given values into the expression and see if it approaches a finite number as (x, y) approaches (0, 0).

Substituting x = 0 and y = 0 into the expression, we get:

(0⁴ - 40(0)²) / ((0)² + 20(0)²)

Since both the numerator and denominator are 0, we have an indeterminate form.

To find the limit, we can simplify the expression by factoring out the common factor of y²:

(x⁴ - 40y²) / (x² + 20y²) = (y²(x² - 40) / (x² + 20y²)

The expression is still indeterminate, so we need to use other methods to find the limit, such as approaching the limit along different paths.

User Sphinks
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