Find the Value of the Limit $\lim _ { x \rightarrow 0 } \left( 1 + x ^ { 2 } \right) ^ { \frac { 1 } { x } }$

question 148

Short Answer

Find the value of the limit $\lim _ { x \rightarrow 0 } \left( 1 + x ^ { 2 } \right) ^ { \frac { 1 } { x } }$ . Use L'Hospital's Rule, if applicable.

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Definitions:

Insufficient Thiamine

A condition resulting from a lack of thiamine (vitamin B1), which can lead to neurological problems and diseases such as beriberi.

Korsakoff's Syndrome

A chronic memory disorder caused by severe deficiency of thiamine (vitamin B1), often linked to alcohol abuse, characterized by memory loss, confabulation, and difficulty acquiring new information.

Insufficient Dopamine

A condition where there is an inadequate level of dopamine in the brain, which can affect mood, movement, and cognition.

Excessive Dopamine

An abnormally high level of dopamine in the brain, which can lead to various disorders, including schizophrenia and addiction.