Evaluate: limx→−2 → − 2 x3+8x+2.

Answer Details

x3+8x+2 $\frac{{\mathrm{<br>}}^{}}{}$

x3 ${}^{\mathrm{<br>}}$ + 8 = x3 ${}^{\mathrm{<br>}}$ + 23
recall that
x3 ${}^3$ + y3 ${}^3$ = (x+y)(x2 ${}^2$ - xy + y2 ${}^2$)
x = x, y = 2
x3 ${}^3$ + 8 = (x+2)(x3 ${}^3$ - 2(x) + 22)

x3+8x+2=(x+2)(x3−2(x)+22)x+2 $\frac{{\mathrm{<br>}}^{}}{}$ - 2x + 4

x = -2
(-2)2 ${}^{\mathrm{<br>}}$ - 2(2) + 4 = 4 - 4 + 4

= 4