Let be such that f(x)+ e^ x+x^2 f(x) e^x+e^ x^2 x>0

MATHEMATICS · Single correct · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Let

f:\mathbb{R}\rightarrow (0,\infty)

be such that

f(x)+\frac{e^{x+x^2}}{f(x)}\leq e^x+e^{x^2}\quad \forall x>0,\text{ then }\lim_{x\rightarrow 1} f(x)\text{ is}

(a) 1 (b)

\frac{1}{e}

(c)

e

(d)

2e