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y = 4x³e^-4x   u = 4x³  v = e^-4x du/dx = 12x² dv/dx = -4e^-4x using the product rule; vdu +udv  vdu + udv = 12x²e^-4x -...

In any sequence, the position of a term (1st, 2nd, 3rd etc.) is represented by the letter ‘n’. In linear sequences only, the ‘nth-term rule’ gives the value of any term in that sequence at position ‘n’. I...

Here as an example of how to make a sentence sound more confident:

“I think this quote from Shakespeare’s ‘Hamlet’ is important because it shows us what virginity meant in Renaissance Engl...

The first thing that we are going to do to tackle this problem is to expand the bracket on the left-hand side (3(m+4)). To do this you have to multiply each of the terms inside the bracket with the 3 that...

The water loses 4200 J/kg °C * 0.5 kg = 2100 J/°C

As it's lost 46,200 J in total (regardless of the time it took for this to happen), it must have reduced in temperature by 46,200 J   /   2100 J/°C...