Difference between revisions of "009A Sample Final 3, Problem 10"

Revision as of 11:03, 6 March 2017

Let $y=\tan(x).$

(a) Find the differential $dy$ of $y=\tan(x)$ at $x={\frac {\pi }{4}}.$

(b) Use differentials to find an approximate value for $\tan(0.885).$ Hint: ${\frac {\pi }{4}}\approx 0.785.$

Foundations:
What is the differential $dy$ of $y=x^{2}$ at $x=1?$
Since $x=1,$ the differential is $dy=2xdx=2dx.$

Solution:

(a)

Step 2:

(b)

Step 1:

Step 2:

(c)

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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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+&nbsp; &nbsp; &nbsp; &nbsp; Since &nbsp;<math style="vertical-align: -4px">x=1,</math>&nbsp; the differential is &nbsp;<math style="vertical-align: -4px">dy=2xdx=2dx.</math>
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