009A Sample Final 3, Problem 4

Discuss, without graphing, if the following function is continuous at  $x=0.$

$f(x)=\left\{{\begin{array}{lr}{\frac {x}{|x|}}&{\text{if }}x<0\\0&{\text{if }}x=0\\x-\cos x&{\text{if }}x>0\end{array}}\right.$

If you think  $f$  is not continuous at  $x=0,$  what kind of discontinuity is it?

Foundations:
$f(x)$  is continuous at  $x=a$  if
$\lim _{x\rightarrow a^{+}}f(x)=\lim _{x\rightarrow a^{-}}f(x)=f(a).$

Solution:

Step 1:

Step 2:

Final Answer:

Return to Sample Exam