Show that x- alimxm-am-xn-an- m-nam-n

L =x→ alimx^m a^mx^n a^n #160; = x→ alimx^m a^mx a. x ax^n a^n #160;we have #160; x^m a^mx a= #160; = ma^m 1 = ma^m 11na^n 1= m ...

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Arithmetic Progression

Show that x...

Question

Show that $l i m x \to a \frac{x^{m} - a^{m}}{x^{n} - a^{n}} = \frac{m}{n} a^{m - n}$

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lim x \to a (\frac{x^{m} - a^{m}}{x^{n} - a^{n}})

l i m x \to a \frac{x^{m} - a^{m}}{x^{n} - a^{n}}

lim x \to a \frac{x^{m} - a^{m}}{x - a} =

lim x \to 1 \frac{x^{m} - 1}{x^{n} - 1}

a = x^{m + n} y^{l}, b = x^{n + l} y^{m} and c = x^{l + m} y^{n}

a^{m - n} b^{n - l} c^{l - m} = 1

x = a^{m + n}, y = a^{n + l} and z = a^{l + m}

x^{m} y^{n} z^{l} = x^{n} y^{l} z^{m}

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