Question

lim->0 1/x-3 + 9x/27-x^3

Answer 1

Solution :

16 ) [tex] \lim_{x \to 3} [ \frac{1}{x-3} + \frac{9x}{27-x^3} ] \\ = \lim_{x \to 3} [ \frac{x^2 +3x+9}{x^3-27} + \frac{9x}{27-x^3} ] \\ = \lim_{x \to 3} [ \frac{9x-x^2 -3x-9}{27-x^3} ] \\ = \lim_{x \to 3} [ \frac{(x-3)^2}{(x-3)(x^2 + 3x+9)} ] \\ = \lim_{x \to 3} [ \frac{x-3}{(x^2 + 3x+9} ] = 0[/tex]

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