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

March 29, 2026Mathematics

ScanSolve AI Answer

March 29, 2026

Answer

$\frac{1}{2}$

Step 1: Divide every term in the numerator and the denominator by the highest power of $K$ , which is $K^2$ . $\lim_{K \to \infty} \frac{K^2 - 2K + 3}{2K^2 + 5K - 3} = \lim_{K \to \infty} \frac{\frac{K^2}{K^2} - \frac{2K}{K^2} + \frac{3}{K^2}}{\frac{2K^2}{K^2} + \frac{5K}{K^2} - \frac{3}{K^2}}$

Step 2: Simplify the terms. $\lim_{K \to \infty} \frac{1 - \frac{2}{K} + \frac{3}{K^2}}{2 + \frac{5}{K} - \frac{3}{K^2}}$

Step 3: Apply the limit. As $K \to \infty$ , terms of the form $\frac{c}{K^n}$ (where $n > 0$ ) approach $0$ . $\frac{1 - 0 + 0}{2 + 0 - 0}$

Step 4: Calculate the final value. $\frac{1}{2}$

The limit is: $\frac{1{2}}$

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Quick Answer

Divide every term in the numerator and the denominator by the highest power of K, which is K^2.

Asked on March 29, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 29, 2026

Step 1: Divide every term in the numerator and the denominator by the highest power of K, which is K^2. _K (K^2 - 2K + 3)/(2K^2 + 5K - 3) = _K (K^2)/(K^2) - (2K)/(K^2) + (3)/(K^2)(2K^2)/(K^2) + (5K)/(K^2) - (3)/(K^2) Step 2: Simplify the terms. _K (1 - 2)/(K) + (3)/(K^2)2 + (5)/(K) - (3)/(K^2) Step 3: Apply the limit. As K , terms of the form (c)/(K^n) (where n > 0) approach 0. (1 - 0 + 0)/(2 + 0 - 0) Step 4: Calculate the final value. (1)/(2) The limit is: (1)/(2)