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Find the limits in Exercises $1-12$.$$\lim _{(x, y) \rightarrow(0,0)} \frac{3 x^{2}-y^{2}+5}{x^{2}+y^{2}+2}$$

$\frac{5}{2}$

Calculus 3

Calculus 1 / AB

Chapter 14

Partial Derivatives

Section 2

Limits and Continuity in Higher Dimensions

Applications of the Derivative

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Find the limits.$$\lim…

we're going to evaluate this limit. We could go ahead and use direct substitution substitution just like we would in a regular one variable limit problem. So we'll go ahead and use X zero and Wyatt zero here. So this is going to be 30 squared minus zero squared, and then we have plus five up top. And so you might already be able to see everything's going to get knocked out except that five in the numerator. And then in the denominator, it's just going to be zero dsquared and mine plus zero squared. And again, the only thing in the denominator that it's going to remain. That's going to be that, too. And so therefore, we're gonna end up with this limit having a value of 2/5.

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