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Question

Question: The value of the limit of \(\frac{x^{3} - x^{2} - 18}{x - 3}\) as x tends to 3 is...

The value of the limit of x3x218x3\frac{x^{3} - x^{2} - 18}{x - 3} as x tends to 3 is

A

3

B

9

C

18

D

21

Answer

21

Explanation

Solution

Let y=limx3x3x218x3=y = \lim_{x \rightarrow 3}\frac{x^{3} - x^{2} - 18}{x - 3} = limx3(x2+2x+6)=9+6+6\lim_{x \rightarrow 3}(x^{2} + 2x + 6) = 9 + 6 + 6

= 21