For what value of L the function is continuous?

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1 Answer
Nov 8, 2017

To make #f# continuous we need #lim_(xrarr4)f(x) =f(4)= L#

Explanation:

So consider the two one-sided limits at #4#.

#lim_(xrarr4^+)f(x) = lim_(xrarr4)(3x-4) = 8#

and

#lim_(xrarr4^-)f(x) = lim_(xrarr4)(x^2-16)/(x-4)#

# = lim_(xrarr4)((x+4)(x-4))/(x-4)#

# = 8#

Make #L = 8#