State the range of values of \(a\) and explain clearly why \(0<b<\dfrac12\).[2]
The diagram shows part of the curve \(y=\ln x\) for \(x>0\). Use the graph to explain how you would obtain a graphical solution for the equation \(x^2=\mathrm e^{4-x}\).[3]
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Answer:(a)(i) \(a=\dfrac{b^2}{1-2b}\). (ii) \(a>0\), \(0<b<\dfrac12\). (b) Draw \(y=2-\dfrac12x\); read the intersection’s \(x\)-coordinate.