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Mathematics-Online problems:

Problem of the week


The function

$\displaystyle f(x) = 1 + \frac{a-bx}{x^3}
$

has a double zero at $ x = 1$ .


\includegraphics[width=.5\linewidth]{TdM_1994_3}


(i)     Determine the parameters $ a$ and $ b$ .
(ii) Determine all zeros of $ f$ .
(iii) Find the area $ A_c$ of the shaded region for $ c = 2$ as well as $ \displaystyle\lim_{c\to\infty} A_c$ .
(iv) Sketch the graph for $ x < 0$ .


Answer:

(i)     Parameters $ a=$ $ ,$ $ b=$
(ii) Another zero $ z=$
(iii) Area $ A_c=$ $ ,$     limiting value $ \displaystyle\lim_{c\to\infty} A_c=$
(iv) The graph of the function for $ x < 0$ is:    not specified

\includegraphics[bb=140 345 481 620,clip,width=.35\linewidth]{TdM_1994_3_2} \includegraphics[bb=140 345 480 630,clip,width=.35\linewidth]{TdM_1994_3_4}
\includegraphics[bb=140 345 480 630,clip,width=.35\linewidth]{TdM_1994_3_3} \includegraphics[bb=140 345 480 620,clip,width=.35\linewidth]{TdM_1994_3_1}


   


[solution to the problem of the previous week]