grandes-ecoles 2024 Q23

grandes-ecoles · France · centrale-maths1__official Taylor series Limit evaluation using series expansion or exponential asymptotics

Let $\varphi$ be the function defined by
$$\forall t \in ] - 1,1 \left[ \backslash \{ 0 \} , \quad \varphi ( t ) = ( 1 - t ) ^ { 1 - 1 / t } \right.$$
Justify that $\varphi$ is extendable by continuity at 0 and specify the value of its extension at 0. We will still denote this extension by $\varphi$.

Let $\varphi$ be the function defined by

$$\forall t \in ] - 1,1 \left[ \backslash \{ 0 \} , \quad \varphi ( t ) = ( 1 - t ) ^ { 1 - 1 / t } \right.$$

Justify that $\varphi$ is extendable by continuity at 0 and specify the value of its extension at 0. We will still denote this extension by $\varphi$.

Paper Questions

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