Limits, Continuity & Differentiability · JEE Main previous year questions

2010 2 questions

1. Q112010 · 25 Apr 2010 · Shift 1

   Let $f:R\to R$ be a continuous function defined by $$f(x)=\frac{1}{e^x+2e^{-x}}$$ Statement - 1 : $f(c)=\frac{1}{3}$, for some $c\in R$. Statement - 2 : $0<f(x)\le \frac{1}{2\sqrt{2}}$, for all $x\in R$

   1. A.Statement - 1 is true, Statement -2 is true; Statement - 2 is not a correct explanation for Statement - 1.
   2. B.Statement - 1 is true, Statement - 2 is false.
   3. C.Statement - 1 is false, Statement - 2 is true.
   4. D.Statement - 1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement - 1.
   Show answer

   Answer: D

2. Q222010 · 25 Apr 2010 · Shift 1

   Let $f:R\to R$ be a positive increasing function with $$\underset{x\to \infty }{\lim }\frac{f(3x)}{f(x)}=1\text{. Then }\underset{x\to \infty }{\lim }\frac{f(2x)}{f(x)}=$$

   1. A.$\frac{2}{3}$
   2. B.$\frac{3}{2}$
   3. C.$3$
   4. D.$1$
   Show answer

   Answer: D