Final answer:
To solve the limit, rationalize the denominator by multiplying the expression by its conjugate and then simplify the result to find the limit as (x,y) approaches (0,0).
Step-by-step explanation:
The student is asking to find the limit of the expression (8x²-6y²)/(√8x²-6y²+1)-1 as (x,y) approaches (0,0). To solve this, we need to rationalize the denominator. The standard way to do this is to multiply the expression by its conjugate over itself, which in this case is (√8x²-6y²-1)/(√8x²-6y²-1). By doing so, we prevent division by zero as the expression approaches the limit by stabilizing the denominator. After rationalizing, simplify the expression and evaluate the limit as (x,y)→(0,0).
Rationalizing the denominator will remove the square root from the denominator. Once the expression is simplified, if the limit exists, the operations can be performed to find the numerical value. If the limit does not exist, then we will enter 'DNE' as the answer.