Consider the function F(x)= x^ 2 -4 x-2

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Consider the function

F(x)=\frac{x^{2}-4}{x-2},

which is undefined at

x=2

. (a) Express

F(x)

in an equivalent algebraic form that is defined for all

x\ne 2

and simplifies evaluation of the limit as

x\to 2

. (b) Using the form obtained in part (a), determine

\displaystyle \lim_{x\to 2} F(x)

. Show each algebraic step and cite any properties of limits you employ. (c) Decide whether

F

can be extended to a continuous function at

x=2

. If so, define

F(2)

so that the extended function is continuous and justify your answer.