Mathematics Mock Test - 10

Consider the function $f(x)=[x+1]-[x]+\frac{1}{x^2-1}$, where $[\cdot ]$ represents the greatest integer function. The function $f(x)$ is decreasing in the interval:

For the function $f(x)=[x+1]-[x]+\frac{1}{x^2-1}$, $f(x)$ has:

The critical points of the function $f(x)=[x+1]-[x]+\frac{1}{x^2-1}$ are:

For the function $f(x)=\frac{x^2}{x^2-1}$, the area formed by the tangent to the curve at $P(2,\frac{4}{3})$ with the coordinate axes is:

The local maximum value of $f(x)=[x+1]-[x]+\frac{1}{x^2-1}$ is: