[" If "f(x)={[mx^(2)+n,,x<0],[nx+m,<=0<=x,1." For what integers "m" and "n" does both "lim_(x rarr0)f(x)],[nx^(3)+m,,x>1]],[" and "lim_(x rarr1)f(x)" exist? "]

if f(x)=3+x,x =1 then lim_(x rarr1)f(x)

f(x)=x,x 0 then find lim_(x rarr0)f(x) if exists

f(x)=(3x^(2)+ax+a+1)/(x^(2)+x-2) and lim_(x rarr-2)f(x) exists.Then the value of (a-4) is

Let f(x)=[x] and g(x)={0,x in Z,x^(2)x in R-Zthen(A)lim_(x rarr1)f(x)exists(B)f(x) is not continuous at x=1(C)lim_(x rarr1)g(x) exists (D) g(x) is continuous at x=1

If f(x)=-sqrt(25-x^(2)) then find lim_(x rarr1)(f(x)-f(1))/(x-1)

If f'(x)=f(x) and f(0)=1 then lim_(x rarr0)(f(x)-1)/(x)=

f(x)={(ax+2, x 1):} , If lim_(x rarr1)f(x) exist then value of a is :

If f(x)=(|x-1|)/(x-1) prove that lim_(x rarr1)f(x) does not exist.

If f(x)=(x^(2))/(1+x^(2)), prove that lim_(x rarr oo)f(x)=1

If f(x)={mx^(2)+n,x 1}. For what integers m and n does both lim_(x rarr0)f(x) and lim_(x rarr1)f(x) exist?