Let `f(x)` be a polynomial of least degree such that `lim_(x->0) (1+ (x^4+f(x^2))/x^3)^(1//x) = e^3`, then write the value of `f(3)`.

The polynomial of least degree such that lim_(xto0)(1+(x^(2)+f(x))/(x^(2)))^(1//x)=e^(2) is

The polynomial of least degree such that lim_(xto0)(1+(x^(2)+f(x))/(x^(2)))^(1//x)=e^(2) is

The polynomial of least degree such that lim_(xto0)(1+(x^(2)+f(x))/(x^(2)))^(1//x)=e^(2) is

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

Let f(x) be a polynomial of least degree such that f(x) ) Lt_(0rarr oo)([x]+[4x]+[9x]+...+[n^(2)x])/(n^(2)) then write the value of Lt_(x rarr0)(18f(x^(2)))/(1-cos3x) Here [^(*)] is gint function.

Let f(x) be a polynomial of degree 4 such that f(1)=1,f(2)=2,f(3)=3,f(4)=4 and lim_(x rarr oo)(xf(x))/(x^(5)+1)=1 then value of f(6) is

The smallest area enclosed by y=f(x) , when f(x) is s polynomial of lease degree satisfying lim_(x->0)[(1+(f(x))/x^3)]^(1/x)=e and the circle x^2+y^2=2 above the x-axis is:

Find a polynomial of least degree, such that underset( x rarr o ) ( "lim") ( 1+ ( x^(2) + f(x))/( x^(2)))^(1//x) = e^(2)