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Question

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,z0
L=limz0(pz+qz+rz+sz4)3/z
which is in the form of 1.

L=elimz0(pz+qz+rz+sz41)×3z
=elimz0(pz1z+qz1z+rz1z+sz1z)×34
=e3/4(logep+logeq+loger+loges)
=e3/4loge(pqrs)
=(pqrs)3/4

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