009A Sample Final 3, Problem 10 - Revision history

Kayla Murray at 23:49, 2 December 2017

2017-12-02T23:49:26Z

Kayla Murray at 16:39, 7 March 2017

2017-03-07T16:39:51Z

Kayla Murray at 16:30, 7 March 2017

2017-03-07T16:30:16Z

Kayla Murray at 19:03, 6 March 2017

2017-03-06T19:03:41Z

Kayla Murray at 02:04, 19 February 2017

2017-02-19T02:04:21Z

Kayla Murray at 02:36, 18 February 2017

2017-02-18T02:36:08Z

Kayla Murray: Created page with "Compute ::a) $\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}$ ::b)
2017-02-18T02:16:52Z

Created page with "Compute ::a) <math style="vertical-align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}</math> ::b) <math st..."

New page
Compute

::a) <math style="vertical-align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}</math>

::b) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin^2x}{3x}</math>

::c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}</math>

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'''Solution:'''

'''(a)'''

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'''(b)'''

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'''(c)'''

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[[009A_Sample_Final_3|'''Return to Sample Exam''']]

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 <span class="exam">(b) Use differentials to find an approximate value for &nbsp;<math style="vertical-align: -5px">\tan(0.885).</math>&nbsp; Hint: &nbsp;<math style="vertical-align: -15px">\frac{\pi}{4}\approx 0.785.</math>
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+<hr>
-!Foundations: &nbsp;
+[[009A Sample Final 3, Problem 10 Solution|'''<u>Solution</u>''']]
-'''Solution:'''
+[[009A Sample Final 3, Problem 10 Detailed Solution|'''<u>Detailed Solution</u>''']]
 [[009A_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

@@ Line 1: / Line 1: @@
-<span class="exam">Let <math>y=\tan(x).</math>
+<span class="exam">Let &nbsp;<math style="vertical-align: -5px">y=\tan(x).</math>
-<span class="exam">(a) Find the differential <math>dy</math> of <math>y=\tan (x)</math> at <math>x=\frac{\pi}{4}.</math>
+<span class="exam">(a) Find the differential &nbsp;<math style="vertical-align: -4px">dy</math>&nbsp; of &nbsp;<math style="vertical-align: -5px">y=\tan (x)</math>&nbsp; at &nbsp;<math style="vertical-align: -15px">x=\frac{\pi}{4}.</math>
-<span class="exam">(b) Use differentials to find an approximate value for <math>\tan(0.885).</math> Hint: <math>\frac{\pi}{4}\approx 0.785.</math>
+<span class="exam">(b) Use differentials to find an approximate value for &nbsp;<math style="vertical-align: -5px">\tan(0.885).</math>&nbsp; Hint: &nbsp;<math style="vertical-align: -15px">\frac{\pi}{4}\approx 0.785.</math>
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 !Step 1: &nbsp;
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+|First, we find &nbsp;<math style="vertical-align: -1px">dx.</math>&nbsp;  We have
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+|&nbsp; &nbsp; &nbsp; &nbsp;<math style="vertical-align: -1px">dx=0.885-\frac{\pi}{4}\approx 0.885-0.785=0.1.</math>
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+|Then, we plug this into the differential from part (a).
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+|So, we have
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+|
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 !Step 2: &nbsp;
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+|Now, we add the value for &nbsp;<math style="vertical-align: -4px">dy</math>&nbsp; to &nbsp;<math style="vertical-align: -16px">\tan\bigg(\frac{\pi}{4}\bigg)</math>&nbsp; to get an
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+|approximate value of &nbsp;<math style="vertical-align: -5px">\tan(0.885).</math>
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+|Hence, we have
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+|
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 !Final Answer: &nbsp;
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-|'''(a)'''
+|&nbsp; &nbsp; '''(a)''' &nbsp; &nbsp; <math style="vertical-align: -5px">dy=2\,dx</math>
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-|'''(c)'''
+|&nbsp; &nbsp; '''(b)''' &nbsp; &nbsp; <math style="vertical-align: -1px">1.2</math>
 |}
 [[009A_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

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 !Foundations: &nbsp;
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+|What is the differential  &nbsp;<math style="vertical-align: -4px">dy</math>&nbsp; of &nbsp;<math style="vertical-align: -4px">y=x^2</math>&nbsp; at &nbsp;<math style="vertical-align: -1px">x=1?</math>
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+|
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 <span class="exam">Let <math>y=\tan(x).</math>
-::<span class="exam">a) Find the differential <math>dy</math> of <math>y=\tan (x)</math> at <math>x=\frac{\pi}{4}.</math>
+<span class="exam">(a) Find the differential <math>dy</math> of <math>y=\tan (x)</math> at <math>x=\frac{\pi}{4}.</math>
-::<span class="exam">b) Use differentials to find an approximate value for <math>\tan(0.885).</math> Hint: <math>\frac{\pi}{4}\approx 0.785.</math>
+<span class="exam">(b) Use differentials to find an approximate value for <math>\tan(0.885).</math> Hint: <math>\frac{\pi}{4}\approx 0.785.</math>
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+|
 |}
 '''Solution:'''
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+|
 |}
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-<span class="exam">Compute
+<span class="exam">Let <math>y=\tan(x).</math>
-::<span class="exam">a) <math style="vertical-align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}</math>
+::<span class="exam">a) Find the differential <math>dy</math> of <math>y=\tan (x)</math> at <math>x=\frac{\pi}{4}.</math>
-::<span class="exam">b) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin^2x}{3x}</math>
+::<span class="exam">b) Use differentials to find an approximate value for <math>\tan(0.885).</math> Hint: <math>\frac{\pi}{4}\approx 0.785.</math>
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