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Please can anybody help me in proving this limit identity? \[ \large \lim_{x \to a}{\frac{x^n - a^n}{x^m - a^m}} = \frac{n}{m}(a)^{n - m} \]

\[ \large \lim_{x \to 0} \frac{2}{3x^2} = \ ? \]

\[\Large \lim_{x \to 0} \frac{x}{|x|} = \ ? \]

\[\large f(x) = \dfrac{(\sqrt{x} + 1)(x^{2} - \sqrt{x})}{x \sqrt{x} + x + \sqrt{x}}\]

Define \(f(x) \) as above and further define ...

If \[ \begin{cases} a + b = 40 \\ b + c = 3 \\ a + c = -11 \end{cases} \] where \(a\), \(b\) and \(c\) are real numbers, and that \( a + b + c = k \), then find ...

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