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

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

The shows the graph of a function

h

, defined for all

x \in \mathbb{R}

except

x = -2

and

x = 3

. The graph has vertical asymptotes at

x = -2

and

x = 3

, a horizontal asymptote at

y = 1

, and a removable discontinuity (hole) at

(1, 2)

, with

h(1) = 4

marked separately.

(a)

State the value of

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

. [1 mark]

(b)

State the value of

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

. [1 mark]

(c)

Determine whether

\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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