If `f(x)=(3x^2+a x+a+1)/(x^2+x-2),` then which of the following can be correct `("lim")_(xvec1)f(x)e xi s t s a=-2` `("lim")_(xvec-2)f(x)e xi s t s a=13` `("lim")_(xvec1)f(x)=4/3` `("lim")_(xvec-2)f(x)=-1/3`

Which of the following is and determinate form (lim)_(xvec1)(x^3-1)/(x-1) b. (lim)_(xvec0)(1+x)^(1//x) c. (lim)_(xvec1)(1/(x^2-1)-1/(x-1)) d. (lim)_(xvec0)(|x|)^(s in R)

Which of the following limits tends to unity? (a) ("lim")_(xvec0)sin(tanx)/(sinx) (b) ("lim")_(xvecpi/2)sin(cosx)/(cosx) ("lim")_(xvec0)"sin"(e^x-1)/x (d) ("lim")_(xvec0)(sqrt(1+x)-sqrt(1-x))/x

If (lim)_(x->2)(f(x-9))/(x-2)=3 then (lim)_(x->2)f(x), is

Evaluate the following: (lim)_(xvec1)[1/(1+x)-3/(1+x^3)]

If f(x)=x((e^(|x|+[x])-2)/(|x|+[x])) then (where [.] represents the greatest integer function) (lim)_(xvec0^+)f(x)=-1 b. (lim)_(xvec0^-)f(x)=0 c. (lim)_(xvec0^)f(x)=-1 d. (lim)_(xvec0^)f(x)=0

Consider the following graph of the function y=f(x). Which of the following is//are correct? (a) lim_(xto1) f(x) does not exist. (b) lim_(xto2)f(x) does not exist. (c) lim_(xto3) f(x)=3. (d)lim_(xto1.99) f(x) exists.

Consider the following graph of the function y=f(x). Which of the following is/are correct? fig.lim_(x rarr1)f(x) does not exist.lim_(x rarr2)f(x) does not exist.lim_(x rarr3)f(x)=3

If lim_(x rarr-2)(f(x))/(x^(2))=1, find (i)lim_(x rarr-2)f(x);(ii)lim_(x rarr-2)(f(x))/(x)

If the function f(x) satisfies lim_(x to 1) (f(x)-2)/(x^(2)-1)=pi , then lim_(x to 1)f(x) is equal to

If lim_(x rarr-2)(f(x))/(x^(2))=1, find (i)lim_(x rarr-2)f(x) and (ii) lim_(x rarr-2)(f(x))/(x)