Question

Lim x-V16-12
D
x4
Plz help

Answer 1

Answer:lim x- √16-x²=32

Explanation:

`x^(4)`-16

=(x²)²-4²

=(x²-4)(x²+4)

=(x²-2²)(x²+4)

=(x-2)(x+2)(x²+4)

So:

`(x^(4)-16 )/(x-2)`=
`((x-2)(x+2)(x^(2)+4) )/((x-2))`=(x+2)(
`x^(2)`+4)

with exclusion:

x
`\\eq`2

Hence:

lim
`(x^(4)-16 )/(x-2)`

x-2

((x+2)(
`x^(2)`+4))=

((2)+2)((2)²+4)=4⋅8=32