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Difference of Powers
$$x^n-a^n=(x-a)(x^{n-1}+x^{n-2}a+\cdots+xa^{n-2}+a^{n-1})$$
Therefore:
$$\lim_{x\to a}\frac{x^n-a^n}{x-a}=na^{n-1}$$
Usage
- Used to remove the indeterminate form $$\frac{0}{0}$$ by factorisation.
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Difference of Powers
$$x^n-a^n=(x-a)(x^{n-1}+x^{n-2}a+\cdots+xa^{n-2}+a^{n-1})$$
Therefore:
$$\lim_{x\to a}\frac{x^n-a^n}{x-a}=na^{n-1}$$
Usage
- Used to remove the indeterminate form $$\frac{0}{0}$$ by factorisation.
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