What is the limit as x approaches-6 of ((4x+3)^{2/3}-9)/(x^2-36) ?

The limit as x approaches-6 of ((4x+3)^{2/3}-9)/(x^2-36) is diverges

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limit as x approaches-6 of ((4x+3)^{2/3}-9)/(x^2-36)

x \to - 6 lim (\frac{( 4 x + 3 ) ^{\frac{2}{3}} - 9}{x ^{2} - 36})

diverges

Solution steps

x \to - 6 lim (\frac{( 4 x + 3 ) ^{\frac{2}{3}} - 9}{x ^{2} - 36})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to - 6 + lim (\frac{( 4 x + 3 ) ^{\frac{2}{3}} - 9}{x ^{2} - 36}) = - ((- 1)^{\frac{2}{3}} \cdot 2 1^{\frac{2}{3}} - 9) \cdot \infty

x \to - 6 - lim (\frac{( 4 x + 3 ) ^{\frac{2}{3}} - 9}{x ^{2} - 36}) = ((- 1)^{\frac{2}{3}} \cdot 2 1^{\frac{2}{3}} - 9) \cdot \infty

= diverges

What is the limit as x approaches-6 of ((4x+3)^{2/3}-9)/(x^2-36) ?
The limit as x approaches-6 of ((4x+3)^{2/3}-9)/(x^2-36) is diverges