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First, label the equations 1 and 2:1: 7x+y=1 and 2: 2x^2-y=3Rearrange equation 2 in terms of yy=2x^2-3Now substitue the rearranged version of equation 2 into 1 to give7x+2x^2-3=1.Bring all the values to t...

The stationary points are located where the gradient of the function is equal to 0. The first derivative of the function describes the gradient so we must differentiate the function to find dy/dx.
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Only factors of 2 are 1 and 2, therefore solution will take form of (2x + a)(x + b) to get 2x² term. Only factors of 3 are 1 and 3 therefore a and b are either 1 or 3. Playing around and intuit...

First notice that no simplifications can be made to the problem without changing the form. We start by factorising the numerator. The highest power of x in this question is 2, therefore we know that it ha...

I would start by asking the student the different forms of integration we know (e.g. substitution, parts).I would then ask the student whether parts or substitution gives the easiest method.If the student...