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Initially, we must recognise the simplest way to integrate this equation is using the 'reverse chain rule' method. 

This means raising the value of the power, in this case '3', by one, and then div...

The first step in tackling this problem is to find the intersection points of the graph with the x and y axes. The y-intercept can be found by substituting x=0 into the function, so y=(0-1)/(0+1)=-1 and t...

dy/dx = (4 * 3)x^(3-1) + 2x^(2-1)*cos(x²)

         = 12x² + 2xcos(x²) 

Plants in hot environments have adaptations to their stomata. These are, having a lower density of stomata and also closing their stomata during the day, when it the environment is warmest. This reduces t...

If the lines are parallel then when the line AB is given in the form y=mx+c then the gradient m of AB is equal to that of the other line. Rearranging the equation for line AB gives y=-(5/3)x-1 so m=-(5/3)...