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If a function \( f(x) \) defined by
[JEE Main-2020 (September)]
\[
f(x)=\left\{\begin{array}{cc}
a e^{x}+b e^{-x} & , \quad-1 \leq x1 \\
c^{2} & , \quad 1 \leq x3 \\
a x^{2}+2 c x & , \quad 3 \leq x \leq 4
\end{array}\right.
\]
P
W
be continuous for some a, b, \( \mathrm{c} \in \mathrm{R} \) and \( \mathrm{f}^{\prime}(0)+\mathrm{f}^{\prime}(2)=\mathrm{c} \), then the value of \( a \) is :
(1) \( \frac{\mathrm{e}}{\mathrm{e}^{2}+3 e+13} \)
(2) \( \frac{e}{e^{2}-3 e+13} \)
(3) \( \frac{e}{e^{2}-3 e-13} \)
(4) \( \frac{e}{e^{2}-3 e+13} \)
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