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Differentiate f(x) = 14x²e^{x^2}To approach this problem we first need to realise that f(x) is made up of two simpler functions multiplied together. This tells us that we should use the...

Here we will want to use the SUVAT equations, which I'm sure you will have come across. Notice that in the question we only have an initial horizontal velocity and because we model all objects as points, ...

a. Finding du_n = u₁ + (n-1)du₄ = u₁ + (4-1)d12 = 3 + 3dd = 3
b. Sum of first 10 termss_n = n/2(2u₁ + (n-1)d)s₁₀ = 5(6 + 9d)...

Derivative of 2xsin(x): 2sin(x)+2xcos(x)Set derivative equal to zero: 2sin(x)+2xcos(x)=0Solve: only valid when x=0Therefore the only stationary point is (0,0) ie the origin.

With this question, it is useful to work with a specific example, so let’s take the recurring decimal 0.27. The first step in converting it to a fraction is to set it equal to x, this will help us with ou...