Question

lim x→2 x⁴-16 iai ?
8- x³

Answer 1

Resposta:

lim (x⁴-16)/(8-x³)

x-->2

(x⁴-16) =(x²-4)*(x²+4)= (x+2)(x-2)*(x²+4)

(2-x)³=2³-12x+6x²-x³

(2-x)³=8-x³-6x*(2-x)

8-x³=(2-x)³+6x*(2-x)

8-x³=(2-x)*[(2-x)²+6x]

8-x³=(2-x)*(4+2x+x²) = -(x-2)*(4+2x+x²)

lim   (x+2)(x-2)*(x²+4) / [ -(x-2)*(4+2x+x²)]

x-->2

lim   (x+2)*(x²+4) / [-(4+2x+x²)]

x-->2

=  (2+2)*(2²+4) / [-(4+2*2+2²)]

= 4*8/[-(4+4+4)] =32/[-12] =- 8/3