Limits, Continuity & Differentiability · JEE Main previous year questions

2015 2 questions

1. Q92015 · 4 Apr 2015 · Shift 1

   Let $f(x)$ be a polynomial of degree four having extreme values at $x=1$ and $x=2$. If ${\lim }_{x\to 0}\left[1+\frac{f(x)}{x^2}\right]=3$, then $f(2)$ is equal to :

   1. A.$0$
   2. B.$4$
   3. C.$-8$
   4. D.$-4$
   Show answer

   Answer: A

2. Q172015 · 4 Apr 2015 · Shift 1

   ${\lim }_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to

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

   Answer: A