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Evaluate(i) (lim)(x->1)(x^(15)-1)/(x^(10...

Evaluate(i) `(lim)_(x->1)(x^(15)-1)/(x^(10)-1)` (ii) `(lim)_(x->0)(sqrt(1+x)-1)/x`

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Let's evaluate the limits step by step. ### Part (i): Evaluate \( \lim_{x \to 1} \frac{x^{15} - 1}{x^{10} - 1} \) **Step 1: Identify the indeterminate form.** When we substitute \( x = 1 \): \[ \frac{1^{15} - 1}{1^{10} - 1} = \frac{0}{0} ...
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