NOTE: denotes the derivative of a) i) . Show that ii) Explain why thus sinh(x) has an inverse function. By expressing as a quadratic in the term ex show sinh-1(x) = b) In experimental work frequently we plot the values using log-log graph paper. i) Suppose our plotted points () lie on a line . By taking exponentials of both sides of this equation find the corresponding relationship between our original data. ii) In a second experiment a straight line plot is not found. Rather the plotted values lie on a steady curve. By estimating the tangent to this curve a relationship of the type is found near the value ). What is the corresponding approximate relationship between x and y for values of x in the vicinity of x0?
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