A rectangular box is to have a square base and a volume of 60 ft3. the material for the base costs 33¢/ft2, the material for the
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It comes from integrating by parts twice. Let
Recall the IBP formula,
Let
Then
Apply IBP once more, with
Notice that the ∫ v du term contains the original integral, so that
Step-by-step explanation:
Given expression is
To, evaluate this limit, let we simplify numerator and denominator individually.
So, Consider Numerator
Clearly, if forms a Geometric progression with first term n and common ratio n respectively.
So, using Sum of n terms of GP, we get
Now, Consider Denominator, we have
can be rewritten as
Now, Consider
So, on substituting the values evaluated above, we get
Now, we know that,
So, using this, we get
Now, in denominator, its an infinite GP series with common ratio 1/e ( < 1 ) and first term 1, so using sum to infinite GP series, we have
Hence,