Difference between revisions of "Exercise 42"

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|-
 
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|Question 1(i)
 
|Question 1(i)
|<math>\ln{(\cos{x})}</math> to <math>x^{6}</math>
+
|<math>\frac{x \ln{\left(1+x\right)}}{\sqrt{1+x}}</math> to <math>x^{4}</math>
 
|-
 
|-
 
|Question 1(ii)
 
|Question 1(ii)
|<math>e^{x}\cos{x}</math> to <math>x^{5}</math>
+
|<math>??</math>
 
|-
 
|-
 
|Question 1(iii)
 
|Question 1(iii)
|<math>\tan{x}</math> to <math>x^{5}</math>
+
|<math>??</math>
 
|-
 
|-
 
|Question 1(iv)
 
|Question 1(iv)

Revision as of 14:11, 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]??[/math]
Question 1(iii) [math]??[/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]