Find the value of `alpha` so that `lim_(x->0)1/(x^2)(e^(alphax)-e^x-x)=3/2`

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

Find the value of limit lim_(x to 0) (x (e^(x) -1))/(1-cosx)

lim_(x->0) ((1+x)^(1/x)-e +(ex)/2)/(x^2)

Find the integral value of n for which lim_(x->0)(cos^2x-cosx-e^xcosx+e^x-(x^3)/2)/(x^n) is a finite nonzero number

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

Evaluate lim_(xto0) (e^(x)+e^(-x)-2)/(x^(2))

Evaluate: lim_(x->0)(e-(1+x)^(1/x))/x

Evaluate the limits lim_(x to 0) (e^(ax)-e^(bx))/x

lim_(xto0)(log(1+3x^(2)))/(x(e^(5x)-1)) =

The value of lim_(x rarr 0) (1-cos2x)/(e^(x^(2))-e^(x)+x) is