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  • web-pythagoras

    https://sheffield.ac.uk/media/30733/download?attachment
    Contents. 1. Introduction 2. 2. The theorem of Pythagoras a2 b2 = c2 2. ... Figure 2 shows squares drawn on thehypotenuse and on the two shorter sides. ... Suppose we wish to find the length, y, of the diagonalof this cuboid. ... From the formula...

  • web-theproductrule

    https://sheffield.ac.uk/media/30814/download?attachment
    In thisunit we will state and use this rule. 2. The product ruleThe rule states:. ... To do this, multiply the second term, topand bottom, by 2(4 x)1/2:. ... We identify u as 1 x3 and v as e2x. We now write down the derivatives. ... Remember that(4...

  • web-logs-exp.dvi

    https://sheffield.ac.uk/media/30816/download?attachment
    δy. δxA. B. f(x). Figure 1.δy. δxis the slope of AB. ... So,it can be taken outside the limit to give:. f ′(x) =1. ... We then. determine what happens toδy. δxin the limit as δx tends to zero. ... tinside the logarithm to give. f(x δx)...

  • web-integrationTRIGsub-.dvi

    https://sheffield.ac.uk/media/30832/download?attachment
    1. IntroductionBy now you should be well aware of the important results that. ... identity sin2x = 1 cos2 x. The reason for doing this will become apparent. ... Let us see what happens when we make the substitution x = tan θ. ... x. The...
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  • web-diffxton.dvi

    https://sheffield.ac.uk/media/30753/download?attachment
    Note that x = x1 and so we use the result with n = 1. ... 3. Some examples requiring the linearity rules 4. 1 c mathcentre August 27, 2004. ... x δx)n = xn nxn1δx. (δx)n. Then, from the formula for the derivative. ... The numbern can be a...

  • web-pascalstriangle-tony

    https://sheffield.ac.uk/media/30810/download?attachment
    Observe the following in the final result:. 3 c mathcentre June 14, 2004. ... 4. The term 2ab arises from contributions of 1ab and 1ba, i.e. ... Either or both of the terms in the binomial expression can be negative. ... With some ingenuity we can...