If `f(1) =g(1)=2`, then `lim_(xto1) (f(1)g(x)-f(x)g(1)-f(1)+g(1))/(f(x)-g(x))` is equal to

If f(1) =g(1)=2 , then lim_(xrarr1) (f(1)g(x)-f(x)g(1)-f(1)+g(1))/(f(x)-g(x)) is equal to

If lim_(xto0)(f(x))/(sin^(2)x)=8,lim_(xto0)(g(x))/(2cosx-xe^(x)+x^(3)+x-2)=lamda" and " lim_(x to 0)(1+2f(x))^((1)/(g(x)))=(1)/(e)," then" lim_(x to 0)(1+f(x))^((1)/(2g(x))) is equal to

f(a)=2,f'(a)=1,g(a)=-1,g'(a)=-2 then lim_(x rarr oo)(g(x)f(a)-g(a)f(x))/(x-a), is

If lim_(xtoa)f(x)=1 and lim_(xtoa)g(x)=oo then lim_(xtoa){f(x)}^(g(x))=e^(lim_(xtoa)(f(x)-1)g(x)) lim_(xto0)((a^(x)+b^(x)+c^(x))/3)^(2/x) is equal to

Let 'f' and 'g' be twice differentiable functions on 'R' and f^(11)(5)=8,g^(11)(5)=2 then lim_(x rarr5)((f(x)-f(5)-(x-5)f^(1)(5))/(g(x)-g(5)-(x-5)g^(1)(5)))

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to