- #1
zorro
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Homework Statement
I have 2 questions-
1) If x>0, show that log(1+x) < x
2) Is the function f(x) = {x} where {.} denotes fractional part of x increasing on [5,6] ?
A1) My book says that we have to construct a function f(x) = x-log(1+x) ans show that it is increasing and f(0)=0 or positive.
I understand the first point but don't get the second. Why should we prove that f(0) >= 0 ?
0 doesnot even lie in the interval (given in question x>0)
A2) Here f(x) is strictly increasing from [5,6), at x=6, function is not continuous and hence derivative doesnot exist.
So the function is not increasing on [5,6] but on [5,6). Is it correct?