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Question: The value of the limit of \(\frac{x^{3} - 8}{(x^{2} - 4)}\) as x tends to 2 is...

The value of the limit of x3−8(x2−4)\frac{x^{3} - 8}{(x^{2} - 4)} as x tends to 2 is

A

3

B

32\frac{3}{2}

C

1

D

0

Answer

3

Explanation

Solution

lim⁡x→2x3−8x2−4=lim⁡x→2(x2+2x+4)(x−2)(x+2)(x−2)=lim⁡x→2x2+2x+4x+2=4+4+42+2=3\lim_{x \rightarrow 2}\frac{x^{3} - 8}{x^{2} - 4} = \lim_{x \rightarrow 2}\frac{(x^{2} + 2x + 4)(x - 2)}{(x + 2)(x - 2)} = \lim_{x \rightarrow 2}\frac{x^{2} + 2x + 4}{x + 2} = \frac{4 + 4 + 4}{2 + 2} = 3.