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a.1000 b. R=62.5 c. Sketch

I would use the whiteboard and write down y=lnx, and also the integration by parts formula below it. I would then explain how to treat ln(x) as the "u" and "1" as dv/dx; including why ...

First of all you must differentiate this function, as this will give you the gradient function necessary to find the gradient at the point (4,16). To differentiate it you use the formula dy/dx= a...

Using the chain rule:If the parameter used is 't', differentiate each equation with respect to 't' so that you have answers for dy/dt, and dx/dt.From the chain rule it is known that: "dy/dx=dy/du * d...

Are we comfortable with an integral being the area under a curve on a graph? Well we'll draw a curve and think about how we could estimate this area. Would you agree that we could chop up the area under t...