Question

Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f continuous at x = a.

f(x)= (x) / (7x^2-x); a= 0

Answer 1

Just find the limit as x approaches zero

\[\lim_{x \rightarrow a} f(x) = x/(7x^2 - x)\]

first lets factor out an x from the bottom and rewrite it as:

f(x) = x/x(7x - 1)

now since you have an x on top and an x on bottom, you can just cancel them out:

= 1/(7x - 1)

now we plug in (a). Since (a) = 0, we can just plug in 0

= 1/(7(0) - 1)
= 1/(0-1)
= 1/-1
= -1

so \[\lim_{x \rightarrow a} f(x) = -1\]

Since f(x) is undefined at 0, but the limit exists, we just need to define f(x) at zero to make it continuous.

f(x) = -1 when x=-1