Question

Evaluate
$\rm \displaystyle \lim_{x\to 1}\ \frac{\sqrt{5x-4}-\sqrt{x}}{x^{3}-1}$

Answer 1

Solution :

$\rm \displaystyle \lim_{x\to 1}\ \frac{\sqrt{5x-4}-\sqrt{x}}{x^{3}-1}$

=Lt {5/[2√(5x-4)]-1/(2√x)}/(3x²)

= $\rm \displaystyle \frac{\frac{5}{2×1}-\frac{1}{2}}{3×1}$

= (4/2)/3

= 2/3

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