Find the value of the limit: lim (x->a) (x^m - a^m) / (x^n - a^n)

May 1, 2026Mathematics

ScanSolve AI Answer

May 1, 2026

Here are the solutions to the limit problems.

We need to find the value of: $\lim_{x \to a} \frac{x^m - a^m}{x^n - a^n}$ Step 1: Recognize the indeterminate form. Substituting $x=a$ into the expression gives $\frac{a^m - a^m}{a^n - a^n} = \frac{0}{0}$ . Step 2: Apply the standard limit formula. We use the formula $\lim_{x \to c} \frac{x^p - c^p}{x - c} = p c^{p-1}$ . We can rewrite the given limit by dividing both the numerator and the denominator

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_x a (x^m - a^m)/(x^n - a^n) Step 1: Recognize the indeterminate form. Substituting x=a into the expression gives (a^m - a^m)/(a^n - a^n) = (0)/(0).

Asked on May 1, 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 May 1, 2026

Here are the solutions to the limit problems. 1. We need to find the value of: _x a (x^m - a^m)/(x^n - a^n) Step 1: Recognize the indeterminate form. Substituting x=a into the expression gives (a^m - a^m)/(a^n - a^n) = (0)/(0). Step 2: Apply the standard limit formula. We use the formula _x c (x^p - c^p)/(x - c) = p c^p-1. We can rewrite the given limit by dividing both the numerator and the denominator