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Unit 3
· Topic 1
Topic 1: Differentiation of exponential and logarithmic functions
Calculus of exponential functions
6 hours
Estimate the limit of 𝑎ℎ−1 ℎ as ℎ → 0, using technology, for various values of 𝑎 > 0.
Recognise that 𝑒 is the unique number 𝑎 for which the above limit is 1.
1 interactive
Recognise and determine the qualitative features of the graph of 𝑦 = 𝑒𝑥, including asymptote and intercept.
Use the rules 𝑑 𝑑𝑥𝑒𝑥 = 𝑒𝑥 and 𝑑 𝑑𝑥𝑒𝑓(𝑥) = 𝑓′(𝑥)𝑒𝑓(𝑥).
1 interactive
Calculus of logarithmic functions
8 hours
Recognise and determine the qualitative features of the graph of 𝑦 = ln(𝑥) = log𝑒(𝑥), including asymptote and intercept.
Recognise and use the inverse relationship of the functions 𝑦 = 𝑒𝑥 and 𝑦 = ln(𝑥).
Solve equations involving exponential and logarithmic functions with base 𝑒, with and without technology.
Use the rules 𝑑 𝑑𝑥ln(𝑥) = 1 𝑥 and 𝑑 𝑑𝑥ln(𝑓(𝑥)) = 𝑓′(𝑥) 𝑓(𝑥).
1 interactive
Model and solve problems that involve derivatives of exponential and logarithmic functions, with and without technology.