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Prove that (root)2 is irrational

The part of syllabus covered by this question is proof by contradiction. Consequently, in order to achieve a contradiction, you can assume that root2 is rational and thus expressed as a/b where a and b are c...
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Answered by Wynn T. • Maths tutor
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Given a second order Differential Equation, how does one derive the Characteristic equation where one can evaluate and find the constants

Given a ODE of the 2nd order, Ay''+by'+cy = 0, we assume the general solution of the exponential form y=e^(mx).As we will see this leads to an easy simplification due to the properties of the exponential . F...
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Answered by William P. • Maths tutor
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Integrate (x^2)(e^x) with respect to x

This is done using the integration by parts method.Answer: (e^x)((x^2) - (2x) - 2) + c
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Answered by Toby P. • Maths tutor
3246 Views

Differentiate 6x^2+2x+1 by first principles, showing every step in the process.

f(x) = 6x 2 +2x+1, f'(x)= [f(x+h)-f(x)]/h here is the original equation and the formula used to differentiate from first principles. For this proof the limit of h is: h=0 and should be stated throughout, but...
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Answered by Thomas N. • Maths tutor
6962 Views

How do I differentiate and integrate powers of x?

For differentiation, we can follow a simple method for differentiating y with respect to x. It may be the case that you have special numbers such as e x you need to differentiate and integrate but these form...
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Answered by Terry T. • Maths tutor
3867 Views