The value of limx→∞(p1/x+q1/x+r1/x+s1/x4)3x, where p,q,r,s>0 is equal to
A
pqrs
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B
(pqrs)3
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C
(pqrs)3/2
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D
(pqrs)3/4
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Solution
The correct option is D(pqrs)3/4 L=limx→∞(p1/x+q1/x+r1/x+s1/x4)3x, where p,q,r,s>0
Put 1x=z
As x→∞,z→0 L=limz→0(pz+qz+rz+sz4)3/z
which is in the form of 1∞.