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1.12 I: Numerical methods (A-level only)

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Question 79

An engineer is monitoring the output voltage V(t)V(t)V(t) of a circuit at different times ttt (measured in seconds). He correctly evaluates:

V(1)=−5 V and V(3)=5 V V(1) = -5 \text{ V and } V(3) = 5 \text{ V} V(1)=−5 V and V(3)=5 V

and concludes that there must be at least one time t∈(1,3)t \in (1, 3)t∈(1,3) where the voltage is zero, due to the change of sign. For which of the following models is this conclusion incorrect?

  • V(t)=5t−10V(t) = 5t - 10V(t)=5t−10
  • V(t)=5t−2V(t) = \frac{5}{t-2}V(t)=t−25​
  • V(t)=54(t−2)3+154(t−2)V(t) = \frac{5}{4}(t-2)^3 + \frac{15}{4}(t-2)V(t)=45​(t−2)3+415​(t−2)
  • V(t)=10t−20t+1V(t) = \frac{10t - 20}{t+1}V(t)=t+110t−20​
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1.12 I: Numerical methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.12 I: Numerical methods (A-level only)

Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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