lim _{x rightarrow 3 / 2} frac{left(4 x^2-6 x | vedclass

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Question

(A) $	ext{આપેલ લક્ષ: } L = \lim _{x ightarrow \frac{3}{2}} \frac{2x(2x-3)(4x^2+6x+9)}{(2x)^{1/3} - 3^{1/3}}$$	ext{છેદનું સંમેયીકરણ કરતા: } a^3 - b

Vedclass · Accepted Answer

$\sqrt[3]{3^{17}}$

Vedclass · Answer

(A) $	ext{આપેલ લક્ષ: } L = \lim _{x ightarrow \frac{3}{2}} \frac{2x(2x-3)(4x^2+6x+9)}{(2x)^{1/3} - 3^{1/3}}$$	ext{છેદનું સંમેયીકરણ કરતા: } a^3 - b^3 = (a-b)(a^2+ab+b^2) 	ext{ જ્યાં } a=(2x)^{1/3}, b=3^{1/3}:$$L = \lim _{x ightarrow \frac{3}{2}} \frac{2x(2x-3)(4x^2+6x+9)((2x)^{2/3} + (6x)^{1/3} + 3^{2/3})}{2x-3}$$L = \lim _{x ightarrow \frac{3}{2}} 2x(4x^2+6x+9)((2x)^{2/3} + (6x)^{1/3} + 3^{2/3})$$x = \frac{3}{2} 	ext{ મુકતા:}$$L = 3(27)(3^{5/3}) = 3^{17/3} = \sqrt[3]{3^{17}}$

$\lim _{x \rightarrow 3 / 2} \frac{\left(4 x^2-6 x\right)\left(4 x^2+6 x+9\right)}{\sqrt[3]{2 x}-\sqrt[3]{3}}=$

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