(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a value for k to make f(x) continuous at 5

f(x)= sqrt(x^{2}-16)-3/(x-5) if x cannot equal 5

3x+k when x=5

2. Relevant equations

none

3. The attempt at a solution

lim x->5 sqrt((x+4)(x-4))-3/(x-5) * sqrt((x+4)(x-4))+3/sqrt((x+4)(x-4))+3

lim x->5 (x+4)(x-4)-9/(x-5)[sqrt((x+4)(x-4))-3]

And that's as far as I got. I'm not sure what my next step should be or if what I did is wrong. I graphed the function and used a program to solve for the limit which is apparently 5/3, but I couldn't come up with that answer. I would really appreciate any help/suggestions. Thanks.

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# Homework Help: Limits and Continuity of a Piecewise Function

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