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

Revision as of 09:57, 5 February 2017

Consider the following function $f:$

f(x)=\left\{{\begin{array}{lr}x^{2}&{\text{if }}x<1\\{\sqrt {x}}&{\text{if }}x\geq 1\end{array}}\right.

a) Find

\lim _{x\rightarrow 1^{-}}f(x).

b) Find

\lim _{x\rightarrow 1^{+}}f(x).

c) Find

\lim _{x\rightarrow 1}f(x).

d) Is

f

continuous at

x=1?

Briefly explain.

Solution:

(a)

Step 1:

Step 2:

(b)

(c)

(d)

@@ Line 1: / Line 1: @@
-<span class="exam">
+<span class="exam">Consider the following function <math> f:</math>
+::::::<math>f(x) = \left\{
+     \begin{array}{lr}
+       x^2 &  \text{if }x < 1\\
+      \sqrt{x} & \text{if }x \geq 1
+     \end{array}
+   \right.
+</math>
+::<span class="exam">a) Find <math> \lim_{x\rightarrow 1^-} f(x).</math>
+::<span class="exam">b) Find <math> \lim_{x\rightarrow 1^+} f(x).</math>
+::<span class="exam">c) Find <math> \lim_{x\rightarrow 1} f(x).</math>
+::<span class="exam">d) Is <math>f</math> continuous at <math>x=1?</math> Briefly explain.
-::<span class="exam">a)
-::<span class="exam">b)
@@ Line 37: / Line 47: @@
 '''(b)'''
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+!Step 1: &nbsp;
+|-
+|
+|-
+|
+|-
+|
+|-
+|
+|}
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+!Step 2: &nbsp;
+|-
+|
+|-
+|
+|-
+|
+|-
+|
+|}
+'''(c)'''
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+!Step 1: &nbsp;
+|-
+|
+|-
+|
+|-
+|
+|-
+|
+|}
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+!Step 2: &nbsp;
+|-
+|
+|-
+|
+|-
+|
+|-
+|
+|}
+'''(d)'''
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Step 1: &nbsp;
@@ Line 66: / Line 126: @@
 |'''(a)'''
 |-
 |'''(b)'''
+|-
+|'''(c)'''
+|-
+|'''(d)'''
 |}
 [[009A_Sample_Midterm_1|'''<u>Return to Sample Exam</u>''']]