Logarithmic functions are useful as measurement units for phenomena with large scale of values, such

Question

Logarithmic functions are useful as measurement units for phenomena with large scale of values, such as decibels (for sound) or Richter scale (for earthquakes). Logarithmic functions make the measurement units smaller and easier to work with. An example of a logarithmic function is given as $y=\ln \left( 1+2x+3{{x}^{2}} \right)$. By using differentiation, find the Maclaurin series for $y$, up to and including the term in ${{x}^{2}}$. [4] By using the standard series in MF26, verify that the answer obtained in part (i) is correct. [2] Find the series expansion of $\frac{x}{\sqrt{4+x}}$, up to and including the term in ${{x}^{3}}$. [4]

Accepted Answer

(a) $\ln(1+2x+3x^2) = 2x + x^2 + \ldots$; (b) $\frac{1}{2}x - \frac{1}{16}x^2 + \frac{3}{256}x^3 + \ldots$

2023 TMJC P2 Q2

2023 TMJC P2 Q2

Video Solution:

Solution:

Solution locked