Difference between revisions of "009A Sample Final 3, Problem 4"

Revision as of 19:33, 17 February 2017

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?

Solution:

(a)

Step 2:

(b)

Step 1:

Step 2:

(c)

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<span class="exam"> Discuss, without graphing, if the following function is continuous at <math>x=0.</math>
-::<span class="exam">a) <math style="vertical-align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}</math>
+::<math>f(x) = \left\{
+     \begin{array}{lr}
+       \frac{x}{|x|} &  \text{if }x < 0\\
+&  \text{if }x = 0\\
+      x-\cos x & \text{if }x > 0
+     \end{array}
+   \right.
+</math>
-::<span class="exam">b) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin^2x}{3x}</math>
+<span class="exam">If you think <math>f</math> is not continuous at <math>x=0,</math> what kind of discontinuity is it?
-::<span class="exam">c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"