Difference between revisions of "009A Sample Final 2, Problem 2"

Revision as of 19:26, 17 February 2017

Let

f(x)=\left\{{\begin{array}{lr}{\frac {x^{2}-2x-3}{x-3}}&{\text{if }}x\neq 3\\5&{\text{if }}x=3\end{array}}\right.

For what values of $x$ is $f$ continuous?

Solution:

(a)

Step 2:

(b)

Step 1:

Step 2:

(c)

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<span class="exam"> Let
-::<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}
-::<span class="exam">b) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin^2x}{3x}</math>
+       \frac{x^2-2x-3}{x-3} &  \text{if }x \ne 3\\
+& \text{if }x = 3
-::<span class="exam">c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}</math>
+     \end{array}
+   \right.
+</math>
+<span class="exam"> For what values of <math>x</math> is <math>f</math> continuous?
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"