help!

[megynbrown1]

Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.

the limit
x -> 0 1/ x + 8 - 1/8 / x

I am getting 1/64

 

[Unco]

Could you chuck in some parentheses ( ) to make it more clear.

 

[megynbrown1]

the limit
x -> 0 1/ (x + 8) - 1/8 / (x)

 

[Unco]

Thanks, Megyn.

\(\displaystyle \mbox{ \lim_{x\to 0} \frac{1}{x + 8} - \frac{1}{8x}}\)

Cross multiplying and adding the fractions gives

\(\displaystyle \mbox{ \lim_{x\to 0} \frac{7x - 8}{8x(x + 8)}}\)

Now consider what the numerator and denominator do as x approaches zero from the left and right.

 

[megynbrown1]

so my answer of 1/64 is way off. i just did it again and got 0.

 

[Unco]

The denominator is tending to zero as x approaches zero; the numerator is non-zero --> the limit does not exist.

(You can consider what happens as x approaches from the left and from the right as an optional exercise, I suppose.)