Question

Evaluate
lim
x²+8
/x+2​

Answer 1

Answer:

Notice,

limx→−∞(x+x2+8x−−−−−−√)

limx→−∞(x+x2+8x)

substituting x=−xx=−x

=limx→∞(−x+x2−8x−−−−−−√)

=limx→∞(−x+x2−8x)

=limx→∞(x2−8x−−−−−−√−x)(x2−8x−−−−−−√+x)(x2−8x−−−−−−√+x)

=limx→∞(x2−8x−x)(x2−8x+x)(x2−8x+x)

=limx→∞x2−8x−x2x2−8x−−−−−−√+x

=limx→∞x2−8x−x2x2−8x+x

=−8limx→∞xx1−8x−−−−−√+x

=−8limx→∞xx1−8x+x

=−8limx→∞xx(1−8x−−−−−√+1)

=−8limx→∞xx(1−8x+1)

=−8limx→∞11−8x−−−−−√+1

=−8limx→∞11−8x+1

=−8(11−0−−−−√+1)

=−8(11−0+1)

=−82=−4