Answer to Question #135021 in Calculus for Alberto Yu

Question

A) Let f(x)=4−x^2 if x≤6 and x−1 if x>6
Find each of the following limits. If the limit does not exist, enter DNE below.
limx→6−f(x)=
limx→6+f(x)=
limx→6f(x)=

Answer 1

• lim_x->6^_f(x) = lim_x->6^_[4-x²]

= lim_h->0[4 - (6-h)²] (here, h is very small positive number tending to zero)

= - 32

• lim_x->6+f(x) = lim_x->6+[x - 1]

= lim_h->0[(6 + h) - 1] (here, h is very small positive number tending to zero)

= 5

• lim_x->6f(x) = DNE because lim_x->6^_f(x) is not equal to lim_x->6+f(x) .