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

1MasterySAQ-SDefinition and calculation of limits6 marksPaper 2~9 min
A chemical processing tank contains a solution that is being heated. The temperature TT (in degrees Celsius) of the solution tt minutes after the heater is turned on is modelled by the function T(t)=120−720t+6,t≥0.T(t) = 120 - \frac{720}{t + 6}, \quad t \geq 0.
(a)
Show that T(0)=0T(0) = 0, and calculate T(6)T(6). [2 marks]
(b)
Determine lim⁡t→∞T(t)\displaystyle\lim_{t \to \infty} T(t) and explain what this value represents in the context of the model. [2 marks]
(c)
The heating element is designed to switch off when the temperature reaches 95 ∘C95\,^\circ\text{C}. Solve T(t)=95T(t) = 95 algebraically to find the time at which this occurs, giving your answer in minutes correct to 3 significant figures. [2 marks]
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