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Find the binomial expansion of (2+x)^3

We know thst the binomial expansion formula is (1+x)ⁿ= 1+nx +(n)(n-1)(x²)/2! ...etc

Thus we want to rearrange the expression we are given into the form (1+x)ⁿso t...

Answered by Laura V. • Maths tutor

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Given that y = 3x(^2) + 6x(^1/3) + (2x(^3) - 7)/(3(sqrt(x))) when x > 0 find dy/dx

Firstly, the (2x(^3) - 7)/(3(sqrt(x))) can be split into (2x(^3))/(3(sqrt(x)) and -7/(3(sqrt(x)). These can then be simplified to (2/3)x(^5/2) and -(7/3)x(^-1/2) respectively. This then gives the equation...

Answered by Samuel H. • Maths tutor

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Integrate, by parts, y=xln(x),

First, we need to separate the RHS as components of U and V. Using the LATE (logarithms, algebra, trigonometry, exponentials) technique, we see that logarithms have priority to algebra hence U = lnx and d...

Answered by Makhdoom S. • Maths tutor

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Suppose a population of size x experiences growth at a rate of dx/dt = kx where t is time measured in minutes and k is a constant. At t=0, x=xo. If the population doubles in 5 minutes, how much longer does it take for the population to reach triple of Xo.

2.925 minutes This question involves solving a first order differential equation via the separation of variables and then substituting in initial conditions in order to find a particular ...

Answered by Scott W. • Maths tutor

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Find the x coordinate of the minimum point of the curve y = e3x - 6e2x + 32.

To find the minimum point of this curve you need to differentiate y and set it equal to zero before solving for x. If the questions does not say otherwise give your answer to 3 s.f. dy/dx = 3e^3x -12e^2x ...

Answered by Hermione W. • Maths tutor

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