Let \( f(x)=1+\int_{0}^{1}\left(x e^{y}+y e^{x}\right) f(y) d y \) where \( x \) and \( y \) are... VIDEO
Let \( f(x)=1+\int_{0}^{1}\left(x e^{y}+y e^{x}\right) f(y) d y \) where \( x \) and \( y \) are independent variables.
If acute angle of intersection of the curves \( \frac{x}{2}+\frac{y}{3}+\frac{1}{3}=0 \) and \( y=f(x) \) be \( \theta \) then \( \tan \theta \) equals to
(a) \( \frac{8}{25} \)
(b) \( \frac{16}{25} \)
(c) \( \frac{14}{25} \)
(d) \( \frac{4}{5} \)
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\[
h(x)=\left\{\begin{arra...