Exercise 42

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Expand the following functions as far as the term indicated:

Question 1(i) [math]\ln{(\cos{x})}[/math] to [math]x^{6}[/math]
Question 1(ii) [math]e^{x}\cos{x}[/math] to [math]x^{5}[/math]
Question 1(iii) [math]\tan{x}[/math] to [math]x^{5}[/math]
Question 1(iv) [math]e^{\sin{x}}[/math] to [math]x^{4}[/math]
Question 1(v) [math]\sin^{2}{x}[/math] to [math]x^{6}[/math]
Question 1(vi) [math]\sin^{-1}{x}[/math] to [math]x^{5}[/math]
Question 1(vii) [math]\sqrt{1+\sin{x}}[/math] to [math]x^{3}[/math]
Question 1(viii) [math]\ln{\left(1+\sin{x}\right)}[/math] to [math]x^{4}[/math]
Question 1(ix) [math]\frac{1}{\sqrt{1-5x}}[/math] to [math]x^{4}[/math]
Question 1(x) [math]\frac{2}{\sqrt[3]{8+3h}}[/math] to [math]h^{3}[/math]
Question 1(xi) [math]\ln{\left(1+e^{x}\right)}[/math] to [math]h^{2}[/math]
Question 1(xii) [math]\tan{-1}{x}[/math] to [math]h^{5}[/math]