" 1acts as a tangent to "y=f(x)" at "x=1/2" and if "P=lim_(x rarr0)(x(x-1))/(f((e^(2x))/(2))-f((e^(-2x))/(2)))" then,"sum_(n=1)^(5)P'

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)

lim_(x rarr0)(x^(2)-1)/(x^(2))

lim_(x rarr0)(2^(2x)-1)/(x)

lim_(x rarr0)(2^(5x)-1)/(x)

lim_(x rarr0)(1+2x)^(5/x)

lim_(x rarr0)((1+x+x^(2))-e^(x))/(x^(2))

lim_(x rarr0)(1+2x)^((1)/(x)) = e^(2)

lim_(x rarr0)(1+x)^((1)/(x))=e

lim_(x rarr0)((e^(x)-x-1)/(x))