Difference between revisions of "009A Sample Final 1, Problem 4"

Latest revision as of 15:46, 2 December 2017

If $y=\cos ^{-1}(2x)$ compute ${\frac {dy}{dx}}$ and find the equation for the tangent line at $x_{0}={\frac {\sqrt {3}}{4}}.$

You may leave your answers in point-slope form.

Solution

Detailed Solution

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@@ Line 1: / Line 1: @@
-<span class="exam"> If
+<span class="exam"> If &nbsp;<math style="vertical-align: -5px">y=\cos^{-1} (2x)</math> compute &nbsp;<math style="vertical-align: -12px">\frac{dy}{dx}</math>&nbsp; and find the equation for the tangent line at &nbsp;<math style="vertical-align: -14px">x_0=\frac{\sqrt{3}}{4}.</math>
-::::::<math>y=x^2+\cos (\pi(x^2+1))</math>
+<span class="exam">You may leave your answers in point-slope form.
-<span class="exam">compute <math style="vertical-align: -12px">\frac{dy}{dx}</math> and find the equation for the tangent line at <math style="vertical-align: -3px">x_0=1</math>. You may leave your answers in point-slope form.
+<hr>
+[[009A Sample Final 1, Problem 4 Solution|'''<u>Solution</u>''']]
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Foundations: &nbsp;
-|-
-|'''1.'''
-|-
-|
-::
-|-
-|'''2.''' What does the Chain Rule state?
-|-
-|
-::
-|}
-'''Solution:'''
+[[009A Sample Final 1, Problem 4 Detailed Solution|'''<u>Detailed Solution</u>''']]
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
-|-
-|First, we compute <math>\frac{dy}{dx}</math>. We get
-|-
-|
-::<math>\frac{dy}{dx}=2x-\sin(\pi(x^2+1))(2\pi x)</math>.
-|}
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 2: &nbsp;
-|-
-|To find the equation of the tangent line, we first find the slope of the line.
-|-
-|Using <math style="vertical-align: -3px">x_0=1</math> in the formula for <math style="vertical-align: -12px">\frac{dy}{dx}</math> from Step 1, we get
-|-
-|
-::<math>m=2(1)-\sin(2\pi)2\pi=2</math>.
-|-
-|To get a point on the line, we plug in <math style="vertical-align: -3px">x_0=1</math> into the equation given.
-|-
-|So, we have <math style="vertical-align: -5px">y=1^2+\cos(2\pi)=2</math>.
-|-
-|Thus, the equation of the tangent line is <math style="vertical-align: -5px">y=2(x-1)+2</math>.
-|}
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Final Answer: &nbsp;
-|-
-|<math>\frac{dy}{dx}=2x-\sin(\pi(x^2+1))(2\pi x)</math>
-|-
-|<math>y=2(x-1)+2</math>
-|}
 [[009A_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]

Difference between revisions of "009A Sample Final 1, Problem 4"

Latest revision as of 15:46, 2 December 2017

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