Question

a) Show that the derivative of y= cosh¹ (ln(-4x)) is: \frac{d y}{d x}=\frac{1}{x} \sqrt{\frac{1}{\ln ^{2}(-4 x)-1}} b) Maclaurin's Series for functions can be expressed as: f(x)=\mathrm{a}_{0}+\mathrm{a}_{1} x+\mathrm{a}_{2} x^{2}+\mathrm{a}_{3} x^{3}+\ldots \ldots i) Find the constants ao, a1₁, a2 and a3 for the following function: f(x)=\sin ^{3}(\ln (1-x)) Using Maclaurin's series, determine the solution for f(x)=sin³ (In(1-x)) when x = 0.25 radian iii) Check and comment on the discrepancy of the answer in part (ii) using a calculator for:f(x)=sin³ (In(1-x)) when x = 0.25 radian[4 Marks]

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