JEE MainMathematicsModerateLimits

The graph of the function y=f(x) has a unique non-vertical
tangent at (e^a, 0) through which the graph passes then
$\lim_{x \rightarrow e^{a}}\mspace{2mu}\frac{\mathcal{l}n(1 + 7f(x)) - sin(f(x))}{3f(x)}$

Show answer and solution

f\left( e^{a} \right) = 0,f^{'}\left( e^{a} \right)\ is\ defined

= \lim_{x \rightarrow e^{a}}\mspace{2mu}\frac{\frac{7f^{'}(x)}{1 + 7f(x)} - cos(f(x)) \cdot f^{'}(x)}{3f^{'}(x)}

= \lim_{x \rightarrow e^{a}}\mspace{2mu}\frac{\frac{7}{1 + 7f(x)} - cos(f(x))}{3} = \frac{7 - 1}{3} = 2

Source: Grass-G / M-28 Mathematics Paper FST 16 Jan.docx

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