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Find the indefinite integral of f(x)=(1-x^2)/(1+x^2)

Int() in this case will refer to integralsAnswer is: f(x)=(1-x^2)/(1+x^2)=(2-(1+x^2)/(1+x^2)=-1+2/(1+x^2)=> Int(f(x))=Int(-1+2/(1+x^2))=Int(-1)+2Int(1/(1+x^2))=-x+2tan^-1(x)+C
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Given that y= x/(2x+5), find dy/dx

Is it integration or differentiation? Differentiation What rule do we use? Since it's a fraction, use the quotient rule Is the rule in the formula book? Yes Identify what u and v equal too. u = x and v = 2x ...
SA
Answered by Salma A. • Maths tutor
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On the same diagram, sketch the graphs of: y = |5x -2| and y = |2x| and hence solve the equation |5x - 2| = |2x|

y = |2x| is a "V" shaped graph with a gradients of 2 and -2 that inflects at the origin (0,0)y = |5x - 2| is a "V" shaped graph with gradients of 5 and -5 that inflects at the point (2/5,...
CP
Answered by Charlie P. • Maths tutor
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Differentiate x^2 from first principles

Differentiation is about finding gradients of functions. With straight lines we take the "rise of run" - the change in y over the change in x. With curves e.g. f(x) = x^2 we need to use the same id...
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How can I calculate the standard deviation of a data set?

The formula for the variance of a data set can be easily remembered by this catchy phrase: 'The mean of the squares minus the square of the mean'. The standard deviation is equal to the square root of the va...
RM
Answered by Robin M. • Maths tutor
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