Evaluate the limit, if it exist

Question

lim (x --> -4)  (1/4 + 1/x)/(4 + x)

 

 

(x/4x + 4/4x)/(4 + x)

 

((x + 4)/4x) / (4 + x)

 

(x + 4)/ (4x(4 + x))

 

(x + 4)/(8x + 4x²)

 

But when I plug in -4, I get zero on the top, I get zero.

 

ANSWER: - 1/16

p107, #23

Answer 1

Hi Mia,

 

Think of (1/4 + 1/x)/(4+x) as a complex fraction. Multiply top and bottom of the "big" fraction by the LCD (4x).

 

Something like this:

 

1/4 + 1/x     (4x)

-----------   ---------

    (4+x)       (4x)

 

That gives:

 

(x + 4)

-------------

 (4+x)4x

 

Since the (x+4) cancels, we have

 

lim_x->-4 1/4x = -1/16.