AP EAMCET201921 Apr 2019Evening ShiftMathematicsLimitsActual
lim x → ∞ x 2 + a x + b - x a < 0 < b
Options
- Adepends on both a and b
- Bdepends only on b
- Cdepends only on a
- Ddoes not depend on a and b
Correct answer
C. depends only on a
Step-by-step solution
lim x → ∞ x 2 + a x + b - x = lim x → ∞ x 2 + a x + b - x × x 2 + a x + b + x x 2 + a x + b + x = lim x → ∞ x 2 + a x + b - x 2 x 2 + a x + b + x = lim x → ∞ a x + b x 2 + a x + b + x = lim x → ∞ x a + b x x 1 + a x + b x 2 + 1 = a 1 + 1 = a 2   ∵ lim x → ∞ 1 x = 0 It depends on a .