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...")
 
 
(10 intermediate revisions by the same user not shown)
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|Question 1(i)
 
|Question 1(i)
<math>\ln{(\cos{x})}</math> to <math>x^{6}</math>
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|<math>\ln{(\cos{x})}</math> to <math>x^{6}</math>
 
|-
 
|-
 
|Question 1(ii)
 
|Question 1(ii)
|Pie
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|<math>e^{x}\cos{x}</math> to <math>x^{5}</math>
 
|-
 
|-
 
|Question 1(iii)
 
|Question 1(iii)
|Ice cream
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|<math>\tan{x}</math> to <math>x^{5}</math>
 
|-
 
|-
 
|Question 1(iv)
 
|Question 1(iv)
|Ice cream
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|<math>e^{\sin{x}}</math> to <math>x^{4}</math>
 
|-
 
|-
 
|Question 1(v)
 
|Question 1(v)
|Ice cream
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|<math>\sin^{2}{x}</math> to <math>x^{6}</math>
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|-
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|Question 1(vi)
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|<math>\sin^{-1}{x}</math> to <math>x^{5}</math>
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|-
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|Question 1(vii)
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|<math>\sqrt{1+\sin{x}}</math> to <math>x^{3}</math>
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|-
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|Question 1(viii)
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|<math>\ln{\left(1+\sin{x}\right)}</math> to <math>x^{4}</math>
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|-
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|Question 1(ix)
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|<math>\frac{1}{\sqrt{1-5x}}</math> to <math>x^{4}</math>
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|-
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|Question 1(x)
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|<math>\frac{2}{\sqrt[3]{8+3h}}</math> to <math>h^{3}</math>
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|-
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|Question 1(xi)
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|<math>\ln{\left(1+e^{x}\right)}</math> to <math>h^{2}</math>
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|-
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|Question 1(xii)
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|<math>\tan^{-1}{x}</math> to <math>h^{5}</math>
 
|}
 
|}
  
\[\lim_{x \to 0} \frac{1-\frac{1}{x}}{1+\frac{1}{x}}\]
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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]