Evaluate `lim_(x,yrarr(1,0))(e^(x-y)+x+y)`

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)))

Evaluate: lim_(x rarr0)(e^(x)-e^(x cos x))/((x+sin x))

Evaluate: lim_(x rarr0)(e^(x)-e^(-x)-2x)/(x^(3))

Evaluate lim_(x rarr0)(log_(e)x)/(x-1)

Evaluate: lim_(x rarr0)(e^(x)+e^(-x)-2)/(x^(2))

Evaluate: "lim_(x rarr0)((e^(x)-e^(-x))/(2))

Evaluate lim_(x rarr0)(e^((1)/(x))-1)/(e^((1)/(x))+1),x!=0

Evaluate: lim_(x rarr0)(y^(2)+sin x)/(x^(2)+sin y^(2)) where (x,y)rarr(0,) along the curve x=y^(2)

Evaluate: lim_(x rarr0)(e-(1+x)^((1)/(x)))/(x)

lim_(x rarr0)((e^(x)-x-1)/(x))