Basic Limits & Continuity | DP IB Maths: AA HL Topic Questions 2021

1a

2 marks

For each of the following, either show that the limit converges and find its value, or else explain why the limit diverges:

\lim_{x \to \frac{2}{5}}

\frac{1}{4 x^{2} - 25}

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1b

2 marks

$\lim_{x \to \frac{5}{2}}$ $\frac{1}{4 x^{2} - 25}$

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1c

3 marks

$\lim_{x \to \frac{5}{2}}$ $\frac{2 x - 5}{4 x^{2} - 25}$

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1a

2 marks

For each of the following, either show that the limit converges and find its value, or else explain why the limit diverges:

\lim_{x \to 4} \frac{1}{x^{2} - 9}

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1b

2 marks

$\lim_{x \to 3} \frac{1}{x^{2} - 9}$

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1c

3 marks

$\lim_{x \to 3} \frac{x - 3}{x^{2} - 9}$

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1a

2 marks

For each of the following, either show that the limit converges and find its value, or else explain why the limit diverges:

\lim_{x \to 0} \tan (x - \frac{π}{4})

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1b

2 marks

$\lim_{x \to \frac{3 π}{4}} \tan (x - \frac{π}{4})$

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1c

3 marks

$\lim_{x \to \frac{3 π}{4}} \frac{\tan (x - \frac{π}{4})}{\sec (x - \frac{π}{4})}$

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DP IB Maths: AA HL