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

Revision as of 21:45, 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 8: / Line 8: @@
     \right.
 </math>
-::<span class="exam">a) Show that <math>f(x)</math> is continuous at <math>x=3</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>.
+<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>.
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