How do you find the limit #lim_(x->-4)((1/4)+(1/x))/(4+x)# ?

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Answer 1 · 2014-08-18T02:42:41

This is a type of problem where the function inside the limit just needs to be simplified until the answer is apparent.

We will simplify the numerator by multiplying the first term by #x/x#, and the second term by #4/4#:

# = lim_(x->-4) ((x/(4x)) + (4/(4x)))/(x+4)#

Now, we can combine the terms:

# = lim_(x->-4) ((x+4)/(4x))/(x+4)#

Simplifying gives us:

# = lim_(x->-4) (x+4)/(4x(x+4))#

The #x+4# term will cancel, leaving us with:

# = lim_(x->-4) 1/(4x)#

The solution is now easily found by substituting #x = -4#:

# = 1/(4*(-4)) = -1/16#