`(lim)_(hto0)((e+h)^(1n(e+h))-e)/hi s____`

lim_(xto0)(e^(ax)-e^(bx))/x

If ("lim")_(xvec0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(("lim")_(xvec0)[1+(f(x))/x]^(1/x))i s____

lim_(xto0)(e^(sinx)-1)/x=

Evaluate lim_(hto0) [(1)/(h^(3)sqrt(8+h))-(1)/(2h)].

lim_(xto0)(e^(x)-e^(-x))/sinx

lim_(x to 0)(e^(sinx)-1)/x=.......

lim_(xto0)(e^(tanx)-e^(x))/(tanx-x)=

lim_(xto1)(e^(x)-e)/(x-1)= ……………

Evaluate lim_(hto0) (log_(e)(1+2h)-2log_(e)(1+h))/(h^(2)).

Show that ("lim")_(xto0) (e^ (1/x)+1 / e^ (1/x)-1) does not exist