Examine whether the followings exist: `lim_(xrarr0)xcosx1/x`

Examine whether the followings exist: lim_(xrarrpi)(sinx)/(pi-x)

Examine whether the followings exist: lim_(xrarr1){x^2+sqrt(x-1)}

Evaluate the following limits: lim_(xrarr0)(x^4+x^2+1)/(x^3-x+2)

Evaluate the following limits: lim_(xrarr3)(x^2-2x+3)

Evaluate the limits: lim_(xrarr0)(1-cosx)/x

Evaluate the limits: lim_(xrarr0)(cosx-cos3x)/x^2

Examine whether the following system of linear equations is consistent or not. If consistent solve the system : 7x+3y=0, 4x-5y=0

Examine whether the following system of linear equations is consistent or not. If consistent, solve the system by using matrix method : 3x-5y=0,2x+y=0

Examine whether the following system of linear equations is consistent or not. If consistent, solve the system by using matrix method : x-4y=0, 2x-8y=0

Examine whether the following systems of linear equations are consistent or not. If consistent, solve the system by Cramer's rule or by using some other method : 2x-y=0, 4x-2y=0