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Question

If f(x)=13{f(x+1)+5f(x+2)} and f(x)>0 for all x R,

then limxf(x) is?

A
25
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B
52
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C
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D
None of the above
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Solution

The correct option is C 52
Let limxf(x)=l, then
limxf(x+1)=limxf(x+2)=l.
Now,
f(x)=13{f(x+1)+5f(x+2)}
limxf(x)=13{limxf(x+1)+5f(x+2)}
l=13(l+5l)
3l2=l2+52l2=5l=52
Hence, option 'B' is correct.

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