`Lt_(x rarr0^(+))(3^(x)-2^(x))/(sqrt(x))`

lim_(x rarr 0)((3^(x)-1)/(sqrt(1+x)-1))

Lt_(x rarr0) (3^(2x)-1)/(x) is equal to

lim_(x rarr0)(1+2x)^(5/x)

Lt_(x rarr0)(sqrt(2+x)-sqrt(2))/(x)

lim_(x rarr0)sqrt(x)=

Lt_(x rarr0)(tan3x)/(2x) is equal to

Lt_(x rarr 0) ((1+x)^(n)-nx-1)/(x^(2)) n gt 1 is euqal to

lim_(x rarr0)((a^(x)-1)/(x))=log_(e)a

Let a= lim _(x rarr 1) (x/(lnx)-1/(xln x)), b = lim _(x rarr 0) ((x^(3)-16x)/(4x+x^(2))), c= lim _(x rarr 1) ((ln(1+sinx))/x) & d = lim _(x rarr -1) ((x+1)^(3))/([sin (x+1) - (x+1)]) Then [[a,b],[c,d]] is

lim_(x rarr0)(2x^2-3x)/x