I have a function of two variables with different limits depending on how they're approached. $$f\left(c,d\right)\equiv\frac{1}{\sqrt{2\pi}}\int_{-d}^{d}\left(e^{-\frac{x^{2}}{2}}-e^{-\frac{x^{2}}{2}+cx^{3}}\right)dx$$
Clearly, $$\lim_{d\rightarrow\infty} f\left(c,d\right)=\infty;c\neq0$$ but $$f\left(c=0,d\right)=0$$ for all d
My question is, is there some functional relationship $c(d)$ where $c\rightarrow0$ as $d\rightarrow\infty$ (like for example, $c\propto1/d^{3}$ ) that would make $$\lim_{d\rightarrow\infty} f\left(c(d),d\right)$$ come out finite and non-zero?