Question

How do you find the limit of `(1/(x+4)-(1/4))/(x)` as `x->0`?

Answer 1

`-1/16`

Explanation:

Find a common denominator within the fractions of the numerator:

`lim_(xrarr0)(1/(x+4)-1/4)/x=lim_(xrarr0)(4/(4(x+4))-(x+4)/(4(x+4)))/x`

`=lim_(xrarr0)(4-(x+4))/(x(4(x+4)))=lim_(xrarr0)(-x)/(4x(x+4))`

`=lim_(xrarr0)(-1)/(4(x+4))`

Now the limit can be evaluated since the `x` has been removed from the denominator:

`=(-1)/(4(0+4))=-1/16`