Limits in the First Principle Differentiation of Exponential Functions

In this post, we estimate the limit of $\frac{a^{h} - 1}{h}$ as $h \rightarrow 0$ using technology, for various values of $a>0$ . This syllabus dot point is a part of the QCE Maths Methods course under the topic Further Differentiation and Applications 2 and sub-part Calculus of Exponential Functions, specifically focussing on the limits in the first principle differentiation of exponential functions.