lim x → ∞ x 2 + a x + b - x a < 0 < b

limx→∞x2+ax+b-xa<0<b
  1. depends on both a and b
  2. depends only on b
  3. depends only on a
  4. does not depend on a and b

Solution

limx→∞x2+ax+b-x

=limx→∞x2+ax+b-x×x2+ax+b+xx2+ax+b+x

=limx→∞x2+ax+b-x2x2+ax+b+x

=limx→∞ax+bx2+ax+b+x

=limx→∞xa+bxx1+ax+bx2+1

=a1+1=a2 ∵limx→∞1x=0

It depends on a.

Asked in: AP EAMCET 2019 (21 Apr Shift 2)

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