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Numerical Methods

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Question 65

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​
[3]
Markscheme

Numerical Methods Questions

  1. A Level
  2. /Maths
  3. /Numerical Methods

80 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.

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