Q. Let $a=\underset {x \rightarrow 1}{\text{Lim}} \frac{x}{\ln x}-\frac{1}{x \ln x} ; b=\underset {x \rightarrow 0}{\text{Lim}} \frac{x^3-16 x}{4 x+x^2} ; c=\underset {x \rightarrow 0}{\text{Lim}} \frac{\ln (1+\sin x)}{x}$ and $d=\underset {x \rightarrow -1}{\text{Lim}}\frac{(x+1)^3}{3(\sin (x+1)-(x+1))}$, then the matrix $\begin{bmatrix}a & b \\ c & d\end{bmatrix}$ is
Matrices
Solution: