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

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

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

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

Evaluate the limits: lim_(xrarrpi/4)(sinx-cosx)/(x-pi/4)

Evaluate the limits: lim_(xrarrpi/4)(sinx-cosx)/(1-tanx)

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

Evaluate the following limits: lim_(xrarr2)(x^2-5x+6)/(x^2-3x+2)

Evaluate the following limits: lim_(xrarr2)(x^8-2^8)/(x^5-2^5)

Evaluate the limits: lim_(xrarrpi/4)(cos2x)/(x-pi/4)

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