IB Maths AA HL 5.1 Limits and derivative concept Question Bank

Practise IB Mathematics SL/HL 5.1 by applying limits and derivative concept methods to exam-style questions.

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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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