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

Mathematics

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Here are the solutions to the limit problems.

  1. We need to find the value of: lim⁡x→axm−amxn−an\lim_{x \to a} \frac{x^m - a^m}{x^n - a^n}

  1. Recognize the indeterminate form.

    Substituting $x=a$ into the expression gives $\frac{a^m - a^m}{a^n - a^n} = \frac{0}{0}$.

  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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