Difference between revisions of "009A Sample Final 1, Problem 8"

Latest revision as of 15:57, 2 December 2017

Let

y=x^{3}.

(a) Find the differential $dy$ of $y=x^{3}$ at $x=2$ .

(b) Use differentials to find an approximate value for $1.9^{3}$ .

Solution

Detailed Solution

Return to Sample Exam

@@ Line 1: / Line 1: @@
 <span class="exam">Let
-::::::<math>y=x^3</math>
+::<math>y=x^3.</math>
-<span class="exam">a) Find the differential <math>dy</math> of <math>y=x^3</math> at <math>x=2</math>.
+<span class="exam">(a) Find the differential &nbsp;<math style="vertical-align: -4px">dy</math>&nbsp; of &nbsp;<math style="vertical-align: -4px">y=x^3</math>&nbsp; at &nbsp;<math style="vertical-align: 0px">x=2</math>.
-<span class="exam">b) Use differentials to find an approximate value for <math>1.9^3</math>.
+<span class="exam">(b) Use differentials to find an approximate value for &nbsp;<math style="vertical-align: -2px">1.9^3</math>.
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+<hr>
-!Foundations: &nbsp;
+[[009A Sample Final 1, Problem 8 Solution|'''<u>Solution</u>''']]
-|-
-|
-|}
-'''Solution:'''
-'''(a)'''
+[[009A Sample Final 1, Problem 8 Detailed Solution|'''<u>Detailed Solution</u>''']]
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
-|-
-|First, we find the differential <math>dy</math>.
-|-
-|Since <math>y=x^3</math>, we have
-|-
-|<math>dy=3x^2dx</math>.
-|}
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 2: &nbsp;
-|-
-|Now, we plug in <math>x=2</math> into the differential from Step 1.
-|-
-|So, we get
-|-
-|<math>dy=3(2)^2dx=12dx</math>.
-|}
-'''(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;
-|-
-|
-|}
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 3: &nbsp;
-|-
-|
-|-
-|
-|}
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Final Answer: &nbsp;
-|-
-|'''(a)''' <math>dy=12dx</math>
-|-
-|'''(b)'''
-|}
 [[009A_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]

Difference between revisions of "009A Sample Final 1, Problem 8"

Latest revision as of 15:57, 2 December 2017

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