Q:

Use the definition of continuity to determine whether f is continuous at a. f(x) = 5x+5 a = -5 Question

Accepted Solution

A:
ANSWER[tex] lim_{x \to - 5}(f(x)) = f( - 5)[/tex]EXPLANATIONIf f(x) is continuous at [tex]x = a[/tex]Then,[tex] lim_{x \to a}(f(x)) = f(a)[/tex]The given function is [tex]f(x) = 5x + 5[/tex][tex]f( - 5) = 5( - 5) + 5[/tex][tex]f( - 5) = - 25 + 5 = - 20[/tex][tex] lim_{x \to - 5}(f(x)) = 5( - 5) + 5[/tex][tex] lim_{x \to - 5}(f(x)) = - 20[/tex]Since,[tex] lim_{x \to - 5}(f(x)) = f( - 5)[/tex]The function is continuous at [tex]x = - 5[/tex]