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Q.

Given  A={x2:xR},B={log23+x2:xR}  andC={x2+3x2:xR}
Given three functions f(x),g(x),h(x) with domain D, where D is ABC. The given functions will follow the inequality f(x)g(x)h(x)   xD{α},where α is fixed positive integer.
And  limxαf(x)=limxαh(x)=l  and  f(α)=h(α)=l
then which of the following is/are not INCORRECT?

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a

The value of limxαg(x) is l.

b

f(α)=g(α)=h(α)=l

c

The value of limxα[g(x)] must be l, where [.] is greatest integer function 

d

The value of g(α) is l

answer is A.

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Detailed Solution

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D is R
 xαLtg(x)=l  from sandwich theorem but g(x)  need not to be l

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