`f(x)=(3x^2+a x+a+1)/(x^2+x-2)` and `lim_(x->-2)f(x)` exists. Then the value of `(a-4)` is__________

If L=lim_(x->2) ((10-x)^(1/3) -2)/(x-2), then the value of |1/(4L)| is

If f(x)=lim_(n->oo)((x^2+a x+1)+x^(2n)(2x^2+x+b))/(1+x^(2n))and lim_(x->+-1)f(x) exist, then The value of b is (a) -1 (b). 1 ( c.) 0 (d). 2

Let ("lim")_(x to1)(x^a-a x+a-1)/((x-1)^2)=f(a)dot Then the value of f(4) is _________

If f(x)=sqrt(4-x^2)+sqrt(x^2-1) , then the maximum value of (f(x))^2 is ____________

If f(x)=sqrt(4-x^2)+sqrt(x^2-1) , then the maximum value of (f(x))^2 is ____________

If f(x)=2x-x^(2) then find the value of f(1)=____.

f(x)=("ln"(x^(2)+e^(x)))/("ln"(x^(4)+e^(2x))) . Then lim_(x to oo) f(x) is equal to

If f(x)=(x^(2)+3x+2)(x^(2)-7x+a) and g(x)=(x^(2)-x-12)(x^(2)+5x+b) , then the value of a and b , if (x+1)(x-4) is H.C.F. of f(x) and g(x) is

Let f ''(x) be continuous at x=0 If ("lim")_(xvec0)(2f(x)-3a(f(2x)+bf(8x))/(sin^2x) exists and f(0)!=0,f^(prime)(0)!=0, then the value of (3a)/b is____