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3(sin x) ^2 cos x

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 -...

(A) express 4^x in terms of y given that 2^x = y. we know that 2² = 4....

This is a common question asked by young students and adults, which demotivates them to study and prevents passion from being the driving force during the tougher chapters. Mathematics is used in every in...

Firstly, we note that a 'root' is simply a solution of the equation (at least, in this case). Let's start from what we've been told: x = 1/2 is a root of the equation. Since it's a solution, let's sub it ...