"Why is Mathematics important, I wont use any of it when I start work?"

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 industry to level that is similar to that of A-Level. Not every piece of information you are taught is directly related to what you will be doing in the future, but being competent in mathematics will demonstrate your logical thinking and problem solving skills. This is one of the "must-have" requirements for all young professionals that are just starting their careers. The fundamental understanding of mathematics helps propel a successful career. So let's Solve the problem.

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Simplify: 3l^2mn+nl^2m−5mn^2l+l^2nm+2n^2ml−mn^2


At t seconds, the temp. of the water is θ°C. The rate of increase of the temp. of the water at any time t is modelled by the D.E. dθ/dt=λ(120-θ), θ<=100 where λ is a pos. const. Given θ=20 at t=0, solve this D.E. to show that θ=120-100e^(-λt)


Calculate the shaded finite region between the curve and the axis for the curve: 3x^2 +11x -4 = 0


Integrate sec^2(x)tan(X)dx