IB Maths AA 5.7 Definitions

This page contains our IB Maths AA definitions for 5.7. By learning each one of these definitions, you will fully cover the content for IB Maths AA 'Advanced limits'.

All Topic 5 Sub-topics 5.1: Introduction To Derivatives 5.2: Applying Derivatives 5.3: Advanced Derivatives 5.4: Introduction To Integration 5.5: Advanced Integration 5.6: Kinematics (HL)5.7: Advanced limits (HL)5.8: Implicit differentiation (HL)5.9: Challenging derivatives (HL)5.10: Challenging integration (HL)5.11: Applying integration (HL)5.12: Differential equations (HL)5.13: Maclaurin series

continuity

A property where the function has no break, jump, or hole at a point, so the limit matches the function value: '

\lim_{x\to a}f(x)=f(a)

converges

Approaches a single finite value as the variable approaches the target value (including as '

x\to\infty

').

differentiability

A property where the function has a well-defined tangent at a point, meaning there is a unique gradient there and the derivative exists.

diverges

Does not approach a single finite value as the variable approaches the target value, so the limit does not exist as a finite number.

Refers to l'Hôpital's rule, which evaluates indeterminate limits of the forms '

\frac{0}{0}

' or '

\frac{\infty}{\infty}

' by differentiating numerator and denominator and taking the new limit, possibly repeatedly.

limit

The value that an expression approaches as the input approaches a specified number or tends to infinity, used to describe behaviour near a point or at an asymptote.

Maclaurin

Describes expressing a function as a power series centred at '

x=0

', used for approximation and for evaluating limits using standard expansions such as '

e^x

', '

\sin x

', and '

\cos x

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