Chapter 2 The coefficients below are given to two decimal places

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2.5 Implicit Differentiation 123
2.5 Implicit Differentiation
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find by implicit differentiation.
a.
b.
c.
d.
e.
____ 2. Find by implicit differentiation.
a.
b.
c.
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124 Chapter 2: Differentiation
d.
e.
____ 3. Find by implicit differentiation.
a.
b.
c.
d.
e.
____ 4. Find by implicit differentiation given that .
a.
b.
c.
d.
e.
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2.5 Implicit Differentiation 125
____ 5. Find by implicit differentiation.
a.
b.
c.
d.
e.
____ 6. Find by implicit differentiation.
a.
b.
c.
d.
e.
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126 Chapter 2: Differentiation
____ 7. Find by implicit differentiation.
a.
b.
c.
d.
e.
____ 8. Evaluate for the equation at the given point . Round your
answer to two decimal places.
a.
b.
c.
d.
e.
____ 9. Find by implicit differentiation given that .
a.
b.
c.
d.
e.
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2.5 Implicit Differentiation 127
____ 10. Evaluate for the equation at the given point . Round
your answer to two decimal places.
a.
b.
c.
d.
e.
____ 11. Find by implicit differentiation given that . Use the original
equation to simplify your answer.
a.
b.
c.
d.
e.
____ 12. Evaluate for the equation at the given point . Round
your answer to two decimal places.
a.
b.
c.
d.
e.
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128 Chapter 2: Differentiation
____ 13. Find the slope of the tangent line at the given point . Round
your answer to two decimal places.
a. 0.67
b. 2.00
c. 1.00
d. 1.67
e. 3.00
____ 14. Find an equation of the tangent line to the graph of the function
at the point .The coefficients below are given to two decimal places.
a.
b.
c.
d.
e.
____ 15. Find an equation of the tangent line to the graph of the function given below at the
given point.
(The coefficients below are given to two decimal places.)
a.
b.
c.
d.
e.
____ 16. Use implicit differentiation to find an equation of the tangent line to the ellipse
at .
a.
b.
c.
d.
e.
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2.5 Implicit Differentiation 129
____ 17. Find in terms of x and y given that . Use the original equation to
simplify your answer.
a.
b.
c.
d.
e.
____ 18. Find in terms of x and y.
a.
b.
c.
d.
e.
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130 Chapter 2: Differentiation
____ 19. Find in terms of x and y given that
a.
b.
c.
d.
e.
____ 20. Find in terms of x and y.
a.
b.
c.
d.
e.
____ 21. Find the points at which the graph of the equation has a vertical or horizontal tangent
line.
a. There is a vertical tangent at but no horizontal tangents.
b. There is a horizontal tangent at and a vertical tangent at .
c. There is a horizontal tangent at but no vertical tangents.
d. There is a horizontal tangent at and a vertical tangent at .
e. There are no horizontal or vertical tangent lines.
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2.5 Implicit Differentiation 131
2.5 Implicit Differentiation
Answer Section

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