Question

Compute the following limit

lim x-->0 ((1/(7+x))-1/7)(1/x)

Answer 1

\[\lim_{x \rightarrow 0}(1/(7+x) - 1/7)/x = -1/49\]Is that the equation you gave?

Answer 2

yes how do you get to this solution

Answer 3

Use L'Hospital rule

Answer 4

my calc class skipped the section on L'Hospital rule so I don't know what that is

Answer 5

First, expand out and simplify the given expression. We end up with:\[\lim_{x \rightarrow 0}(1/(x(x+7)) - 1/7x)\]Then, rewrite it as (using partial fractions) as:\[\lim_{x \rightarrow 0}-x/(7x^{2} + 49x)\]Factor the constants and x out, you get:\[-(\lim_{x \rightarrow 0}(1/(7(7+x))) = -1/7(\lim_{x \rightarrow 0}(1/(x+7) = (-1/7)(1/7) = -1/49\]

Answer 6

You can also simplify your fraction to become
\[-\frac{1}{7 (x+7)}
\]

Answer 7

Also, L'Hopital is not appliable to this. It's not a indetermination of infi/infi or 0/0, it's (1/7)/0, right?

Answer 8

Oops, (-1/7)/0

Answer 9

thank you very much for your help