Evaluate
`underset(xrarrinfty)Lt(cosx)/x`

Evaluate: underset(xrarr0)lim (cos2x-1)/(cosx-1)

Evaluate underset(xrarr0)Lt [cosx] if it exists. Here [] denotes the greatest integer function.

Evaluate: underset(xrarrpi/4)lim (cosx-sinx)/(x-pi/4) .

Let f: R rarr R be a positive increasing function with underset(xrarrinfty)lim(f(3x))/(f(x))=1, then underset(xrarrinfty)lim(f(2x))/(f(x)) =

Evaluate: underset(xrarr0)lim (x(e^x-1))/(1-cosx)

Evaluate underset(xto0)lim(e^(x^(2))-cosx)/(x^(2))

True or False : If underset(x rarr a)Lt f(x)g(x) exists then both underset(xrarra^+)Lt f(X) and underset(xrarra^-) Lt g(x) exist separately.

Evaluate: underset(0)overset(pi)int(e^(cosx))/(e^(cosx)+e^(-cosx))dx

Evaluate: underset(0)overset(pi)int(dx)/(5+4cosx)

Evaluate: underset(0)overset(pi//2)int(x)/(sinx+cosx)dx