`lim_(x rarr 0)(1+x(1+f(x)/(k x^2))^(1//x)=e^3` and ` f(4)=64` then `k` has value

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

Let f(x) be a polynomial of least degree such that lim_(x rarr0)(1+(x^(4)+f(x^(2)))/(x^(3)))^(1/x)=e^(3), then write the value of f(3)

If f(x) is a polynomial of least degree,such that lim_(x rarr0)(1+(f(x)+x^(2))/(x^(2)))^((1)/(x))=e^(2), then f(2) is

If lim_(x rarr0)[1+x+(f(x))/(x)]^((1)/(x))=e^(3), then find the value of 1n(lim_(x rarr0)[1+(f(x))/(x)]^((1)/(x)))is=-

If lim_(x rarr0)[1+x+(f(x))/(x)]^((1)/(x))=e^(3), then the value of ln(lim_(x rarr0)[1+(f(x))/(x)]^((1)/(x))) is

lim_(x rarr0)(e^(x)-1-x-((x^(2))/(2)))/(x^(3))=6k

If f(x) is a polynomial of degree 6, which satisfies lim_(x rarr0)(1+((f(x))/(x^(3))))^((1)/(x))=e^(2) and local minimum at x=1 and has local maximum at x=0 and x=2, then the value of ((5)/(9))^(4)f((18)/(5)) is :

lim_(x rarr0)((ln(1+x^(2)+x^(4)))/((e^(x)-1)x)

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