IIT JEE 1983 Maths - 'Adapted' - FIB to Single-Digit Integer Q3

Calculus Level 4

For the function f ( x ) = { x 1 + e 1 / x , x 0 0 , x = 0 f(x)=\begin{cases} \large\frac{x}{1+e^{1/x}},\ \normalsize x\neq0 \\ \normalsize 0,\ x=0 \end{cases} the derivative from the left f ( 0 ) = p f'(0^-)=p and the derivative from the right f ( 0 + ) = q f'(0^+)=q . Find 3 p + q 3p+q .


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The answer is 3.

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