A function is defined for all real numbers by f(x)= x^ 2 -16 x-4

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

A function

f

is defined for all real numbers by

f(x)=\frac{x^{2}-16}{x-4}.

A new function

F

is created by setting

F(x)=f(x)

for

x\neq 4

and defining

F(4)

so that

F

becomes continuous at

x=4

. (a) Compute

\displaystyle\lim_{x\to 4}f(x)

, showing your algebraic work. (b) Determine the value that must be assigned to

F(4)

so that

F

is continuous at

x=4

and justify your selection using the definition of continuity.