Evaluate `("lim")_(xvec0)(3x+|x|)/(7x-5|x|)`

Evaluate lim_(xto0) (3x+|x|)/(7x-5|x|).

lim_(xrarr0) (3x+|x|)/(7x-|x|) , is

Evaluate: lim_(xto0)(sin 3x)/(sin 7x)

Evaluate: (lim)_(xvec 0)(log(5+x)-log(5-x))/(x)

Evaluate lim_(x rarr 0)(sin(3x))/(x)

Evaluate: lim_(x rarr0)(tan2x-x)/(3x-sin x)

Evaluate lim_(x rarr0)(tan3x-2x)/(3x-sin^(2)x)

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

Let f(x)={cos[x],xgeq0|x|+a ,x<0 The find the value of a , so that ("lim")_(xvec0) f(x) exists, where [x] denotes the greatest integer function less than or equal to x .

Evaluate lim_(x to 0) ("sin"5x)/("sin"7x)