jee-advanced 2008 Q5

jee-advanced · India · paper1 Differentiating Transcendental Functions Determine parameters from function or curve conditions

Let $g ( x ) = \frac { ( x - 1 ) ^ { n } } { \log \cos ^ { m } ( x - 1 ) } ; 0 < x < 2 , m$ and $n$ are integers, $m \neq 0 , n > 0$, and let $p$ be the left hand derivative of $| x - 1 |$ at $x = 1$.
If $\lim _ { x \rightarrow 1 + } g ( x ) = p$, then
(A) $n = 1 , m = 1$
(B) $n = 1 , m = - 1$
(C) $n = 2 , m = 2$
(D) $n > 2 , m = n$

Let
$g ( x ) = \frac { ( x - 1 ) ^ { n } } { \log \cos ^ { m } ( x - 1 ) } ; 0 < x < 2 , m$ and $n$ are integers, $m \neq 0 , n > 0$, and let $p$ be the left hand derivative of $| x - 1 |$ at $x = 1$.

If $\lim _ { x \rightarrow 1 + } g ( x ) = p$, then\\
(A) $n = 1 , m = 1$\\
(B) $n = 1 , m = - 1$\\
(C) $n = 2 , m = 2$\\
(D) $n > 2 , m = n$

Paper Questions

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