If `3x+2y=1` is a tangent to `y=f(x)` at `x=1//2`, then `lim_(xrarr0) (x(x-1))/(f((e^(2x))/(2))-f((e^(-2x))/(2)))`

If 3x+2y=1 acts as a tangent y=f(x)atx=(1)/(2) and if p=lim_(x rarr0)(x(x-1))/(f((e^(2x))/(2))-f((e^(-2x))/(2))) then sum_(r=1)^(oo)p^(r)=......... (A) (1)/(2)(B)(1)/(3)(C)(1)/(6)(D)(1)/(7)

What is lim_(xrarr0)[e^(x^2]-1]/(x^2)

The value of lim_(xrarr0) ((1+2x)/(1+3x))^((1)/(x^(2))).e^((1)/(e^(x))) is

The value of lim_(xrarr0) ((1+2x)/(1+3x))^((1)/(x^(2))).e^((1)/(e^(x))) is

If the equation of the normal to the curve y=f(x) at x=0 is 3x-y+3=0 then the value of lim_(xrarr0) (x^(2))/({f(x^(2))-5f(4x^(2))+4f(7x^(2))}) is

Lim_(xrarr0)(f(Cosx))/(x^2) =? where f(x) = (1-x)/(1+x)

If f(x)=3x^(2)-7x+5 , then lim_(xrarr0)(f(x)-f(0))/(x) is equal to

If f(3)=2 then lim_(xrarr2)f(x^2-1) = …........