(Solved): Curve sketching for the function \[ f(x)=\frac{x^{2}-1}{e^{x}} \] a) What is the domain of \( f(x) ...

Curve sketching for the function \[ f(x)=\frac{x^{2}-1}{e^{x}} \] a) What is the domain of \( f(x) \). b) Is the function odd, even or neither odd nor even? c) What are the zeros of \( f(x) \) ? d) What are the poles of \( f(x) \) ? e) Calculate the first three derivatives of \( f(x) \). f) Determine the turning points of \( f(x) \). g) Determine the inflection points of \( f(x) \). h) What is the limit of \( f(x) \) for \( x \rightarrow \pm \infty \) ?