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Name of student | Date | ||||
Adm. number | Year/grade | Stream | |||
Subject | Pure Mathematics 1 (P1) | Variant(s) | P11, P12, P13 | ||
Start time | Duration | Stop time |
Qtn No. | 1 | Total |
---|---|---|
Marks | 11 | 11 |
Score |
Question 1 Code: 9709/13/M/J/18/11, Topic: Differentiation, Integration
The diagram shows part of the curve $y=(x+1)^{2}+(x+1)^{-1}$ and the line $x=1$. The point $A$ is the minimum point on the curve.
$\text{(i)}$ Show that the $x$-coordinate of $A$ satisfies the equation $2(x+1)^{3}=1$ and find the exact value of $\displaystyle\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}$ at $A$. $[5]$
$\text{(ii)}$ Find, showing all necessary working, the volume obtained when the shaded region is rotated through $360^{\circ}$ about the $x$-axis. $[6]$