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Question

Let f(a)=g(a)=k and their nth derivatives fn(a), gn(a) exist and are not equal for some n. Further if limxaf(a)g(x)f(a)g(a)f(x)+g(a)g(x)f(x)=4, then the value of k is:


A

4

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B

2

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C

1

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D

0

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Solution

The correct option is A

4


limxaf(a)g(x)f(a)g(a)f(x)+g(a)g(x)f(x)=4Applying L' Hospital rulelimxaf(a).g(x)g(a).f(x)g(x)f(x)=4limxakg(x)kf(x)g(x)f(x)=4limxak[g(x)f(x)]g(x)f(x)=4k=4


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