The correct option is C 54 To find lim_x→ 12x 2/√(26+x) 3 The above limit can be written is a 00 form.Thus, applying L'Hosptial's Rule, we get ...

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Formation of Algebraic Expressions

limx→ 12x-2/√...

Question

$lim x \to 1 \frac{2 x - 2}{\sqrt[3]{26 + x} - 3} =$

54

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50

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48

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Solution

The correct option is C $54$
To find $lim x \to 1 \frac{2 x - 2}{\sqrt[3]{26 + x} - 3}$
The above limit can be written is a $\frac{0}{0}$ form.
Thus, applying L'Hosptial's Rule, we get

$lim x \to 1 \frac{2}{{\frac{1}{3} (26 + x)}^{- 2 / 3}}$

Or, $lim x \to 1 6 (26 + x)^{2 / 3}$

Thus, $lim x \to 1 6 (27)^{2 / 3}$

$= 6 \times (27)^{2 / 3}$

$= 6 \times 9 = 54$

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