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

Practise IB Mathematics HL 5.1 by applying limits and derivative concept methods to questions from the Question Bank.

Exam points

Estimate limits from numerical tables or graphs and explain the limiting behaviour without relying on formal analytic limit methods.
Interpret a derivative as the gradient function or rate of change, using dy/dx, f′(x), dV/dr and ds/dt notation in context.

[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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