Let be the function p(t) = cases t^ 2 -4 t-2 , & t 2, L, & t = 2

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

Problem

Let

p

be the function

p(t) = \begin{cases} \dfrac{t^{2}-4}{t-2}, & t \neq 2, \\ L, & t = 2, \end{cases}

where

L

is a constant. (a) Compute

\displaystyle \lim_{t\to 2} p(t)

. (b) Determine the value of

L

that makes

p

continuous at

t=2

, and verify your conclusion using the formal definition of continuity.