Let the function $ f(x) $ be defined as follows: $$ f(x) = \begin{cases} (1 + | \sin x |)^{\frac{a}{|\sin x|}}, & -\frac{\pi}{6}<x<0 \\b, & x = 0 \\ \frac{\tan 2x}{\tan 3x}, & 0<x<\frac{\pi}{6} \end{cases} $$ Then the values of $ a $ and $ b $ are:
LIST I | LIST II | ||
A. | \(\lim\limits_{x\rightarrow0}(1+sinx)^{2\cot x}\) | I. | e-1/6 |
B. | \(\lim\limits_{x\rightarrow0}e^x-(1+x)/x^2\) | II. | e |
C. | \(\lim\limits_{x\rightarrow0}(\frac{sinx}{x})^{1/x^2}\) | III. | e2 |
D. | \(\lim\limits_{x\rightarrow\infty}(\frac{x+2}{x+1})^{x+3}\) | IV. | ½ |
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.