IB Maths AA SL 5.1 Limits and Derivative Concept Questions

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

Exam points

interpret f′(x) as an instantaneous rate of change or tangent gradient and evaluate it at a stated point
use derivative values and limiting behaviour to determine rates such as height, distance or population change
evaluate derivative limits, including behaviour as the independent variable approaches infinity, and state the result with context

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Study SL 5.1—Limits and derivative concept conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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Let $f(x)=\frac{2 x-6}{1-x}$ , for $x \neq 1$ .

Find $\lim _{x \rightarrow \infty} f(x)$ .

valid approach
eg recognizing that $\lim _{x \rightarrow \infty}$ is related to the horizontal asymptote, table with large values of x, their y value from (a)(iii), L'Hopital's rule $\lim _{x \rightarrow \infty} f(x)=-2$

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IB Maths AA SL 5.1 Limits and Derivative Concept Questions question 1