You're viewing 1 free preview question for Maths AI SL — subscribe to unlock 75 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

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

1MasterySAQ-SDefinition and calculation of limits6 marksPaper 2~9 min
A particle moves along a straight line. Its displacement, ss metres, from a fixed point OO at time tt seconds is given by s(t)=t2−1t−1,t≥0, t≠1.s(t) = \frac{t^2 - 1}{t - 1}, \quad t \geq 0,\ t \neq 1.
(a)
State why s(t)s(t) is undefined at t=1t = 1. [1 mark]
(b)
Show that lim⁡t→1s(t)=2\displaystyle\lim_{t \to 1} s(t) = 2. [2 marks]
(c)
The function s(t)s(t) has a removable discontinuity at t=1t = 1. A student claims that redefining s(1)=2s(1) = 2 allows the instaneous velocity of the particle at t=1t = 1 to be calculated, and that this velocity equals 1 m s−11\ \text{m\,s}^{-1}. Determine whether the student's claim is correct. [3 marks]
diagram

Solutions

Questions 2-76

Unlock these questions with Premium

Sign Up →

That's every free question here — 1 of 76.

+75 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade