Difference between revisions of "009A Sample Final 2, Problem 4"

Revision as of 19:27, 17 February 2017

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

3x^{2}+xy+y^{2}=5

at the point

(1,-2)

Solution:

(a)

ExpandStep 2:

(b)

ExpandStep 1:

ExpandStep 2:

(c)

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-<span class="exam">Compute
+<span class="exam">Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
-::<span class="exam">a) <math style="vertical-align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}</math>
+::<span class="exam"><math>3x^2+xy+y^2=5</math> at the point <math>(1,-2)</math>
-::<span class="exam">b) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin^2x}{3x}</math>
-::<span class="exam">c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}</math>
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