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] |
Find expansions as far as the term indicated for:
| Question 1(i) | [math]\frac{x \ln{\left(1+x\right)}}{\sqrt{1+x}}[/math] to [math]x^{4}[/math] |
| Question 1(ii) | [math]\sqrt{1-x} \sin{x}[/math] to [math]x^{4}[/math] |
| Question 1(iii) | [math]e^{x} \sin{3x}[/math] to [math]x^{4}[/math] |
| Question 1(iv) | [math]e^{x} \ln{\left(1+x\right)}[/math] to [math]x^{3}[/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] |
