Difference between revisions of "Exercise 42"
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(Created page with "Expand the following functions as far as the term indicated: {| class="wikitable" |- |Question 1(i) <math>\ln{(\cos{x})}</math> to <math>x^{6}</math> |- |Question 1(ii) |Pie...") |
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| (10 intermediate revisions by the same user not shown) | |||
| Line 4: | Line 4: | ||
|- | |- | ||
|Question 1(i) | |Question 1(i) | ||
| − | <math>\ln{(\cos{x})}</math> to <math>x^{6}</math> | + | |<math>\ln{(\cos{x})}</math> to <math>x^{6}</math> |
|- | |- | ||
|Question 1(ii) | |Question 1(ii) | ||
| − | | | + | |<math>e^{x}\cos{x}</math> to <math>x^{5}</math> |
|- | |- | ||
|Question 1(iii) | |Question 1(iii) | ||
| − | | | + | |<math>\tan{x}</math> to <math>x^{5}</math> |
|- | |- | ||
|Question 1(iv) | |Question 1(iv) | ||
| − | | | + | |<math>e^{\sin{x}}</math> to <math>x^{4}</math> |
|- | |- | ||
|Question 1(v) | |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: |
| + | {| class="wikitable" | ||
| + | |- | ||
| + | |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> | ||
| + | |} | ||
Latest revision as of 14:13, 1 August 2020
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] |
