Evaluate: `lim_(xrarr0)x^x`

lim_(xrarr0)x sec x

Evaluate: lim_(xrarr0) (2^x-9^x-3(x+1))/(sqrt2- sqrt1+cosx)

lim_(xrarr0) x sec x

Evaluate: lim_(xrarr0) (tan x-sin x)/(x^(3))

Evaluate lim_(xrarr0) (1+x)^(1/x)

Evaluate lim_(xrarr0)((3^(x)-2^(3x))/(x)).

Evaluate lim_(xrarr0)((1+x)^(n)-1)/(x)

Evaluate: (i)lim_(xrarr0)((e^(-x)-1)/(x))(ii)lim_(xrarr0)((e^(x)-e^(-x))/(x))(iii)lim_(xrarr0)((e^(x)+e^(-x)-2)/(x^(2)))

If f(x) is defined as f(x)={{:(2x,+,3,x,le 0),(3x,+,3,x,le0):} then evaluate : lim_(xrarr0) f(x) "and" lim_(xrarr1) f(x)

Evaluate lim_(xrarr0)((x^(3)cotx)/(1-cosx)).