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Limits Continuity and Differentiability question

2024 · 4 Apr · Shift 1 · Q54

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JEE Main
Mathematics
Limits Continuity and Differentiability
2024 · 4 Apr · Shift 1 · Q54

Limits Continuity and Differentiability question

2024 · 4 Apr · Shift 1 · Q54

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

If

\lim_{x \rightarrow 1} \frac{(5 x+1)^{1 / 3}-(x+5)^{1 / 3}}{(2 x+3)^{1 / 2}-(x+4)^{1 / 2}}=\frac{\mathrm{m} \sqrt{5}}{\mathrm{n}(2 \mathrm{n})^{2 / 3}}

, where

\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1

, then

8 \mathrm{~m}+12 \mathrm{n}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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