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If y = 2/3 x^3 + x^2; a) What is dy/dx? b) Where are the turning points? c) What are the nature of the turning points?

a) By simple parametric differentiation of each term, dy/dx = 2x^2 + 2x b) The condition for a turning point is the gradient (dy/dx) at that point is zero. 0 = x(2x + 2) so either x=0 or 2x+2=0. Therefore th...
AF
Answered by Annabel F. • Maths tutor
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Integrate x*sin(x) with respect to x.

We integrate by parts: u=x u'=1; v'=sin(x) v=-cos(x) integral(x sin(x)dx) = -x cos(x) + integral(cos(x)dx) = -x*cos(x) + sin(x) + C where C is a constant.
JR
Answered by James R. • Maths tutor
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How do I do binomial expansions for positive integer n?

The general method for (a+b)^n is: 1)write out pascals triangle (see whiteboard) and stop at the nth row. Write this on a line. 2)write down the powers of a in ascending order (and simplify) 3)write down the...
DR
Answered by Daniel R. • Maths tutor
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How do I work out what integration method I should use to solve an integral?

A-Level Mathematics is about a wide range of topics, among which Integrating is key! While differentiation is a technique, whereby a set of rules can be used to approach problems, integration is an art, for ...
LC
Answered by Luigi C. • Maths tutor
12776 Views

Show that x^2 - x +2 is positive for all values of x

(x-1/2) 2 = (x-1/2)(x-1/2)=x 2 -x+1/4, add 7/4 to get x 2 -x+2 therefore x 2 -x+2 = (x-1/2) 2 + 7/4 squared numbers always positive so (x-1/2) 2 >= 0 therefore (x-1/2) 2 + 7/4 is always positive
PM
Answered by Pearse M. • Maths tutor
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