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Divide every term in the numerator and the denominator by the highest power of K, which is K².

March 29, 2026Mathematics

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Answer

\frac{1}{2}

4 steps

Divide every term in the numerator and the denominator by the highest power of $K$ , which is $K^2$ .
$\lim_{K \to \infty} \frac{K^2 - 2K + 3}{2K^2 + 5K - 3} = \lim_{K \to \infty} \frac{\frac{K^2}{K^2} - \frac{2K}{K^2} + \frac{3}{K^2}}{\frac{2K^2}{K^2} + \frac{5K}{K^2} - \frac{3}{K^2}}$
Simplify the terms.
$\lim_{K \to \infty} \frac{1 - \frac{2}{K} + \frac{3}{K^2}}{2 + \frac{5}{K} - \frac{3}{K^2}}$
Apply the limit.
As $K \to \infty$ , terms of the form $\frac{c}{K^n}$ (where $n > 0$ ) approach 0.
$\frac{1 - 0 + 0}{2 + 0 - 0}$
Calculate the final value.
$\frac{1}{2}$

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