Question

Lim x->-2 x^3+8/x+2=

Answer 1

12

Explanation:

note that x³ + 8 is a sum of cubes and factors as

x³ + 8 = (x + 2)(x² - 2x + 4), thus

lim x → - 2
`(x^3+8)/(x+2)`

= lim x → - 2
`((x+2)(x^2-2x+4))/(x+2)`

Cancel factor (x + 2) on numerator/denominator

= lim x → - 2 (x² - 2x + 4) ← evaluate by direct substitution

= (- 2)² - 2(- 2) + 4 = 4 + 4 + 4 = 12

Answer 2

because ( (-2)³+8))/(-2+2)=0/0,

you use formula a³+b³°(a+b)(a²-ab+b²).

therefore (x³+8)/(x+2) = ( (x+2)(x²-2x+4))/(x+2) = x²-2x+4

so lim x->-2 (x²-2x+4) = (-2)²-2*(-2)+4=

=4+4+4=12.