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X tends to 2 x^3+8/x+2 |
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Answer» Answer: Notice how you have a difference of two cubes. x 3 − y 3 = x 3 + x 2 y + x y 2 − x 2 y − x y 2 − y 3 = ( x − y ) ( x 2 + x y + y 2 )
In our expression, we have y = 2 : ( x ) 3 − ( 2 ) 3 x − 2 = ( x − 2 ) ( x 2 + 2 x + 4 ) x − 2 = x 2 + 2 x + 4 At this point, the LIMIT can be evaluated: ⇒ lim x → 2
x 3 − 8 x − 2
= lim x → 2
x 2 + 2 x + 4
= ( 2 ) 2 + 2 ( 2 ) + 4
= 4 + 4 + 4
= |
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