FunctionHard

Question

Let f : R+ →R be a negative decreasing function
with limx→∞fx-x36f(x)=k then limx→∞fsinxf(x) is

Options

A.

less than k

B.

greater than k
 

C.

equal to k

D.

Nothing can be said

Solution

x-x36<x∀x>0⇒fx-x36>f(sinx)>f(x)⇒fx-x36f(x)<f(sinx)f(x)<1⇒limx→∞fx-x36f(x)<limx→∞f(sinx)f(x)<1

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