# 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: $$$$\frac{1-exp(-\kappa(T-t))}{\kappa}\rightarrow(T-t) \quad \rm{when\space} \kappa \rightarrow 0$$$$

Thanks in advance!

• You should ask this question in other site – user16651 Jul 11 '16 at 12:04

## 1 Answer

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

• That is a brilliant way to do it (ofc it has to be defined for both denominator and numerator for kappa)! – Donkey_JOHN Jul 11 '16 at 12:14
• Ok it is brilliant way :D :D :D – user16651 Jul 11 '16 at 12:16
• :) It's called l'Hospital rule @Donkey_JOHN, see: en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule – Quantuple Jul 11 '16 at 13:04