Let f:R+→R be defined by f(x)=e3x−3+lnx+tan−1(x−1) and g be th – InterviewSolution

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1.	Let f:R+→R be defined by f(x)=e3x−3+lnx+tan−1(x−1) and g be the inverse function of f. If limx→1x5−5g(x)g′(x)sin(x−1)=pq where p,q∈N, then the least possible value of (p−5q) is
Answer» Let $f : R^{+} \to R$ be defined by $f (x) = e^{3 x - 3} + ln x + {tan}^{- 1} (x - 1)$ and $g$ be the inverse function of $f .$ If $lim x \to 1 \frac{x^{5} - 5 g (x) g^{'} (x)}{sin (x - 1)} = \frac{p}{q}$ where $p, q \in N,$ then the least possible value of $(p - 5 q)$ is

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