Difference between revisions of "009A Sample Final 1, Problem 2"

Revision as of 21:22, 1 February 2016

Consider the following piecewise defined function:

f(x)=\left\{{\begin{array}{lr}x+5&{\text{if }}x<3\\4{\sqrt {x+1}}&{\text{if }}x\geq 3\end{array}}\right.

a) Show that

f(x)

is continuous at

x=3

.

b) Using the limit definition of the derivative, and computing the limits from both sides, show that

f(x)

is differentiable at

x=3

.

Foundations:

Solution:

(a)

(b)

Step 2:

Step 3:

(c)

Step 1:

@@ Line 1: / Line 1: @@
+<span class="exam"> Consider the following piecewise defined function:
+::::::<math>f(x) = \left\{
+     \begin{array}{lr}
+       x+5 &  \text{if }x < 3\\
+\sqrt{x+1} & \text{if }x \geq 3
+     \end{array}
+   \right.
+</math>
+::<span class="exam">a) Show that <math>f(x)</math> is continuous at <math>x=3</math>.
+::<span class="exam">b) Using the limit definition of the derivative, and computing the limits from both sides, show that <math>f(x)</math> is differentiable at <math>x=3</math>.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Foundations: &nbsp;