 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2016/2/a/solution

x = 1

x \to 1 lim \frac{2 ^{x} - 2}{x - 1} = \frac{d}{d x} 2^{x}_{x = 1} = 2 ln 2.

Here

2^{x} = e^{x l n 2}

and the chain rule supplies the factor

ln 2

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