Question about continuity: f(x) = 1/x + 1/7 for x != -7, c for x = -7; find c

[Farhat]

\(\displaystyle \mbox{For what value of the constant }\, c\, \mbox{ is the following function}\)

\(\displaystyle \mbox{continuous at }\, x\, =\, -7?\)

. . . . .\(\displaystyle f(x)\, =\, \begin{cases}\dfrac{1}{x}\, +\, \dfrac{1}{7}&\mbox{if }\, x\, \neq\, -7 \\ {}&{} \\ c&\mbox{if }\, x\, =\, -7 \end{cases}\)

Can someone help me understand what steps should be taken to deal with this problem?

 

[Harry_the_cat]

You need to find the limit of \(\displaystyle \frac{\frac{1}{x}+\frac{1}{7}}{x+7} \)as x approaches -7.

Add the two fractions in the numerator first, tidy up the algebra and then see what you can do from there.

c must equal this limit for the function to be continuous.