Difference between revisions of "009A Sample Midterm 3, Problem 1"

Revision as of 09:45, 5 February 2017

Find the following limits:

a) If

\lim _{x\rightarrow 3}{\bigg (}{\frac {f(x)}{2x}}+1{\bigg )}=2,

find

\lim _{x\rightarrow 3}f(x).

b) Find

\lim _{x\rightarrow 0}{\frac {\tan(4x)}{\sin(6x)}}.

c) Evaluate

\lim _{x\rightarrow \infty }{\frac {-2x^{3}-2x+3}{3x^{3}+3x^{2}-3}}.

Solution:

(a)

Step 1:

Step 2:

(b)

(c)

Step 1:

Step 2:

@@ Line 1: / Line 1: @@
-<span class="exam">
+<span class="exam">Find the following limits:
-::<span class="exam">a)
+::<span class="exam">a) If <math>\lim _{x\rightarrow 3} \bigg(\frac{f(x)}{2x}+1\bigg)=2,</math> find <math>\lim _{x\rightarrow 3} f(x).</math>
-::<span class="exam">b)
+::<span class="exam">b) Find <math>\lim _{x\rightarrow 0} \frac{\tan(4x)}{\sin(6x)}. </math>
+::<span class="exam">c) Evaluate <math>\lim _{x\rightarrow \infty} \frac{-2x^3-2x+3}{3x^3+3x^2-3}. </math>
@@ Line 55: / Line 56: @@
 |-
 |
+|-
+|
+|-
+|
+|}
+'''(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;
 |-
 |
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 |'''(a)'''
 |-
 |'''(b)'''
+|-
+|'''(c)'''
 |}
 [[009A_Sample_Midterm_3|'''<u>Return to Sample Exam</u>''']]