IB Maths AA HL Sl 5 1 Limits and Derivative Concept Questions

Review the concept of a limit and interpret derivatives as graph gradients or rates of change, focusing on slope values and population growth comparisons.

Exam points

Read f'(a) as the graph's slope at x=a, including horizontal and straight sloping sections
Interpret dP/dt as the population's instantaneous rate of change with respect to time
Compare models using derivative values at the same time and explain which population grows faster

[Maximum number: 2]

A function f is defined by $f(x)=\arcsin \left(\frac{x^{2}-1}{x^{2}+1}\right), x \in \mathbb{R}$ .

By considering limits, show that the graph of y=f(x) has a horizontal asymptote and state its equation.

as $x \rightarrow \pm \infty, f(x) \rightarrow \arcsin 1\left(\rightarrow \frac{\pi}{2}\right)$
so the horizontal asymptote is $y=\frac{\pi}{2}$

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IB Maths AA HL Sl 5 1 Limits and Derivative Concept Questions question 1