e^(x)((1)/(x^(2))-(2)/(x^(3)))

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

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...

A : (a-b)/(a)+(1)/(2)((a-b)/(a))^(2)+(1)/(3)((a-b)/(a))^(3)+....=log_(e)((a)/(b)) R : log_(e)(1-x)=-x-(x^(2))/(2)-(x^(3))/(3)-(x^(4))/(4)-....

int(e^(x))/(x^(4))dx=-(e^(x))/(3)[(1)/(x^(3))+(1)/(2x^(2))+(1)/(2x)]+(1)/(6)int(e^(x))/(x)dx

Prove that, int (e^(x))/(x^(4))dx=-(e^(x))/(3)[(1)/(x^(3))+(1)/(2x^(2))+(1)/(2x)]+(1)/(6)int (e^(x))/(x)dx .

The value of lim_(x rarr0)((1+2x)/(1+3x))^((1)/(x^(2)))*e^((1)/(x)) is e^((5)/(2))b.e^(2)ce^(-2)d.1

Let f(x)=-4.sqrt(e^(1-x))+1+x+(x^(2))/(2)+(x^(3))/(3) . If g(x) is inverse of f(x) then the value of (1)/(g^(')(-(7)/(6))) is

Let f(x)=-4.sqrt(e^(1-x))+1+x+(x^(2))/(2)+(x^(3))/(3) . If g(x) is inverse of f(x) then the value of (1)/(g^(')(-(7)/(6))) is

If the function f(x)=-4e^((1-x)/(2))+1+x+(x^(2))/(2)+(x^(3))/(3) and g(x)=f^(-1)(x) then the reciprocal of g'((-7)/(6)) is