Prove that `y = ((x+1)(x-2)) / (x(x +3)) ` can ahve any value in `(- oo, oo)` for `x in R`.

If lim_(x->oo) f(x) exists and is finite and nonzero and if lim_(x->oo) {f(x)+(3f(x)−1)/(f^2(x))}=3 ,then the value of lim_(x->oo) f(x) is

If lm_(x->oo) f(x) exists and is finite and nonzero and if lim_(x->oo) {{f(x)+(3f(x)−1)/(f_2(x))}=3 ,then the value of lim_(x->oo) f(x) is

If lim_(x->oo) f(x) exists and is finite and nonzero and if lim_(x->oo) {f(x)+(3f(x)−1)/(f^2(x))}=3 ,then find the value of lim_(x->oo) f(x)

Let f(x)=x^2-2x-1 AA x in R Let f:(-oo, a]->[b, oo) , where a is the largest real number for which f(x) is bijective. If f : R->R , g(x) = f(x) + 3x-1 , then the least value of function y = g(|x|) is

If y=x+(x^(2))/(2)+(x^(3))/(3)+....oo , then x =

If y=x+(x^(2))/(2)+(x^(3))/(3)+....oo , then x =

Let f(x)=x^2-2x-1 AA xinR Let f:(-oo, a]->[b, oo) , where a is the largest real number for which f(x) is bijective. If f : R->R , g(x) = f(x) + 3x-1 , then the least value of function y = g(|x|) is

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

The range of (x ^ (2) -2x + 3) / (x ^ (2) -2x-8) AA x in R is (i) (- oo, 0] uu [1, oo) (ii) [ (1) / (2), 2] (iii) (- oo, - (2) / (9)] uu [1, oo) (iv) (oo, -6] uu ([- 2, oo)

If y = x^(x ^(x^(x ^(x.... oo) then prove that x dy/dx = y^2/(1- y logx )