If `G(x) = -sqrt(25-x^2)` then `lim_(x to 1) (G(x)-G(1))/(x-1) = ?`

lim_(x to 0) (pi^(x)-1)/(sqrt(1+x)-1)

If f(x) =cot ^(-1) ((3x -x^(3))/(1-3x^(2))) and g (x) =cos ^(-1) ((1- x ^(2))/(1+x^(2))) then lim _(xtoa) (f(x) -f(a))/(g (x) -g(a)) is equal to-

If f (a) = 2 , f'(a) = 1, g (a) = -1 and g'(a) = 2 , show that lim_(x to a)(g(x)f(a)-f(x)g(a))/(x-a) = 5

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

If G(x)=.-sqrt(25-x^(2)),"find the value of " underset(xrarr1)"lim"(G(x)-G(1))/(x-1)

Let g(x) be a function defined on [-1,1]dot If the area of the equilateral triangle with two of its vertices at (0,0) a n d (x ,g(x)) is (a) (sqrt(3))/4 , then the function g(x) is (b) g(x)=+-sqrt(1-x^2) (c) g(x)=sqrt(1-x^2) (d) g(x)=-sqrt(1-x^2) g(x)=sqrt(1+x^2)

If lim _(xto0)(f(x))/(sin ^(2)x) = 8, lim _(xto0) (g(x))/( 2 cos x-ye ^(x) + x^(3) +x-2)=lamda and lim _(xto0) (1+2f(x)) ^((1)/(g(x)))=1/e, then lamda=

If f(x)=2/(x-3),g(x)=(x-3)/(x+4) , and h(x)=-(2(2x+1))/(x^2+x-12) then lim_(x->3)[f(x)+g(x)+h(x)] is (a) -2 (b) -1 (c) -2/7 (d) 0

If f (a) =2, f '(a) =1, g (a) =-3 .g'(a) =-1 , then the value of lim _(xtoa)(f(a) g(x) -g(a)f(x))/(a-x) is equal to-

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)xg(x)) lim_(xto0)((x-1+cosx)/x)^(1/x) is equal to