# Getting closer to the powers of $$e$$!

Calculus Level 4

Let $$g:\mathbb{R}\to\mathbb{R}$$ be a differentiable function such that $$g(2)=-40$$ and $$g^{\prime}(2)=-5$$. Then find the value of $$\displaystyle \lim _{ x\to 0 }{ { \left( \dfrac { g\left( 2-{ x }^{ 2 } \right) }{ g\left( 2 \right) } \right) }^{\frac { 4 }{ { x }^{ 2 } } } }$$.

Notation:

• $$g^{\prime}(x)$$ denotes the first derivative of $$g(x)$$.
• $$e \approx 2.718$$ is the Euler's number.
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