Answer:lim x- √16-x²=32
Step-by-step explanation:
[tex]x^{4}[/tex]-16
=(x²)²-4²
=(x²-4)(x²+4)
=(x²-2²)(x²+4)
=(x-2)(x+2)(x²+4)
So:
[tex]\frac{x^{4}-16 }{x-2}[/tex]=[tex]\frac{(x-2)(x+2)(x^{2}+4) }{(x-2)}[/tex]=(x+2)([tex]x^{2}[/tex]+4)
with exclusion:
x[tex]\neq[/tex]2
Hence:
lim [tex]\frac{x^{4}-16 }{x-2}[/tex]
x-2
((x+2)([tex]x^{2}[/tex]+4))=
((2)+2)((2)²+4)=4⋅8=32
