If p, q, r, s 0 , then lim x → ∞ p 1 x + q 1 x + r 1 x + s 1 x 4 3 x is equal to

Question

If p, q, r, s > 0 , then lim x → ∞ p 1 x + q 1 x + r 1 x + s 1 x 4 3 x is equal to, pqrs, pqrs 3, pqrs 3 2, pqrs 3 4

MARKS App · Accepted Answer

Consider the given expression, lim x → ∞ p 1 x + q 1 x + r 1 x + s 1 x 4 3 x [where, p, q, r, s > 0] Put, 1 x = z , so that x → ∞ ⇒ z → 0 = lim z → 0 p z + q z + r z + s z 4 3 z which is in the form 1 ∞ . =e lim z → 0 p z + q z + r z + s z 4 − 1 3 z = e lim z → 0 p z - 1 z + q z - 1 z + r z - 1 z + s z - 1 z 3 4 = e 3 4 log e p + log e q + log e r + log e s = e 3 4 log e pqrs = pqrs 3 4

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