iran-konkur 2015 Q114

iran-konkur · Other · konkur-riazi_1394 Sign Change & Interval Methods
114- What is the value of $\displaystyle\lim_{x \to 0}\left([2x]+[-2x]\right)\dfrac{1-\cos^2 x}{1-\sqrt{1+x^2}}$? (The symbol $[\,]$ denotes the floor function.)
p{4cm} p{4cm} p{3cm}} (1) $-2$(2) $2$(3) zero(4) does not exist.

\textbf{114-} What is the value of $\displaystyle\lim_{x \to 0}\left([2x]+[-2x]\right)\dfrac{1-\cos^2 x}{1-\sqrt{1+x^2}}$? (The symbol $[\,]$ denotes the floor function.)

\begin{tabular}{p{4cm} p{4cm} p{4cm} p{3cm}}
(1) $-2$ & (2) $2$ & (3) zero & (4) does not exist.
\end{tabular}

\medskip