# How to understand the following limits when kapa limits to Zero

The equation is quite simple, however it is not very obvious to me to have the following relationship: $$$$\frac{1-exp(-\kappa(T-t))}{\kappa}\rightarrow(T-t) \quad \rm{when\space} \kappa \rightarrow 0$$$$

:D Is it a joke? $$\underset{\kappa \to 0 }{\mathop{\lim }}\,\frac{1-e^{-\kappa(T-t)}}{\kappa}=\underset{\kappa \to 0 }{\mathop{\lim }}\,\frac{\frac{d}{d\kappa}\left(1-e^{-\kappa(T-t)}\right)}{\frac{d}{d\kappa}\kappa}=\underset{\kappa \to 0 }{\mathop{\lim }}\,(T-t) e^{-\kappa(T-t)}=T-t$$