Eye Of The Pi

Calculus Level pending

If f ( x ) = x e x f(x) = xe^x , evaluate the expression f ( π + 1 ) f ( π ) \dfrac{f(\pi+1)}{f'(\pi)}

Give your answer to 3 decimal places.


The answer is 2.718.

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1 solution

f ( x ) = x e x f ( x ) = ( x + 1 ) e x f ( x + 1 ) = ( x + 1 ) e x + 1 = ( x + 1 ) e x e f ( x + 1 ) f ( x ) = e , x R { 1 } \\ f(x) = xe^x\\f'(x) = (x+1)e^x\\f(x+1)=(x+1)e^{x+1}=(x+1)e^x \cdot e\\\\\dfrac{f(x+1)}{f'(x)}= e, \; \forall x \in \mathbb{R}- \left \{ -1 \right \}

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