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Limits and Continuity · Paper 2 — Free Maths AA HL Practice Questions

What this topic covers

Calculus is where AA HL stops rewarding memorised algebra and starts rewarding process. Every mark scheme in this topic is built around specific words — show that, hence, determine, justify — and examiners are trained to withhold marks the instant your working skips a step, even when your final answer is correct. The four subtopics here build on each other in a strict chain: limits define continuity, continuity is the gatekeeper for differentiability, derivatives feed every application (tangents, optimisation, kinematics), and integration — the reverse process — feeds differential equations. Learn it in that order and the HL-only material (implicit differentiation, integration by parts, volumes of revolution, and the whole of differential equations) stops looking like extra content and starts looking like the natural next question.

Read the full Calculus lesson notes →

1MasterySAQ-SDefinition and calculation of limits6 marksPaper 2~9 min

The below shows the graph of

y = h(x)

for

-3 \leq x \leq 5

. The graph has vertical asymptotes at

x = -2

and

x = 3

(a)

State the value of

\displaystyle\lim_{x \to -2^{-}} h(x)

. [1 mark]

(b)

State the value of

\displaystyle\lim_{x \to +\infty} h(x)

. [1 mark]

(c)

Determine whether

\displaystyle\lim_{x \to 1} h(x)

exists. If it does, state its value. [2 marks]

(d)

Given that

h(1) = 4

, determine whether

h

is continuous at

x = 1

. Justify your answer. [2 marks]

Solutions

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