The value of a for which `lim_(x->-2)(3x^2+a x+a+3)/(x^2+x-2)` exists. Also find the value of the limit.

The value of a for which lim_(x rarr-2)(3x^(2)+ax+a+3)/(x^(2)+x-2) exists.Also find the value of the limit.

If a in I , then value of a for which lim_(xrarra) (tan([x^(2)]-[x]^(3)))/((x-a)^(3)) exists finitely, is /are

If a in I , then value of a for which lim_(xrarra) (tan([x^(2)]-[x]^(3)))/((x-a)^(3)) exists finitely, is /are

Evaluate the following limit: (lim)_(x->3)(x^2-4x+3)/(x^2-2x-3)

If lim_(x rarr oo)(a+b sin x-cos x+ce^(x))/(x^(3)) exists find the values of a,b,c. Also find the limit

The value of the limit lim_(x rarr ∞)((x-1)/(x+3))^(x+2) is

Evaluate the limits: lim_(xrarr2)(3x^2-2x-8)/(x^2-6x+8)

If (x^2+x−2)/(x+3) -1) f(x) then find the value of lim_(x->-1) f(x)

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)