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Deck 11: Extension D: Partial Derivatives

Question

Let

Let and suppose that changes from to (a)Compute (b)Compute <div style=padding-top: 35px>

and suppose that

Let and suppose that changes from to (a)Compute (b)Compute <div style=padding-top: 35px>

changes from

Let and suppose that changes from to (a)Compute (b)Compute <div style=padding-top: 35px>

to

Let and suppose that changes from to (a)Compute (b)Compute <div style=padding-top: 35px>

(a)Compute

Let and suppose that changes from to (a)Compute (b)Compute <div style=padding-top: 35px>

(b)Compute

Let and suppose that changes from to (a)Compute (b)Compute <div style=padding-top: 35px>

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Question

Find the differential of the function

Find the differential of the function <div style=padding-top: 35px>

Question

Find the differential of the function

A)

<strong>Find the differential of the function </strong> A) B) C) D) <div style=padding-top: 35px>

B)

<strong>Find the differential of the function </strong> A) B) C) D) <div style=padding-top: 35px>

C)

<strong>Find the differential of the function </strong> A) B) C) D) <div style=padding-top: 35px>

D)

<strong>Find the differential of the function </strong> A) B) C) D) <div style=padding-top: 35px>

Question

Find the equation of the tangent plane to the given surface at the specified point.

A)

<strong>Find the equation of the tangent plane to the given surface at the specified point. </strong> A) B) C) D) E) <div style=padding-top: 35px>

B)

<strong>Find the equation of the tangent plane to the given surface at the specified point. </strong> A) B) C) D) E) <div style=padding-top: 35px>

C)

<strong>Find the equation of the tangent plane to the given surface at the specified point. </strong> A) B) C) D) E) <div style=padding-top: 35px>

D)

<strong>Find the equation of the tangent plane to the given surface at the specified point. </strong> A) B) C) D) E) <div style=padding-top: 35px>

E)

<strong>Find the equation of the tangent plane to the given surface at the specified point. </strong> A) B) C) D) E) <div style=padding-top: 35px>

Question

Find the equation of the tangent plane to the given surface at the specified point.

Find the equation of the tangent plane to the given surface at the specified point. <div style=padding-top: 35px>

Question

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height cm if the tin is 0.04 cm thick.<div style=padding-top: 35px>

cm if the tin is 0.04 cm thick.

Question

Find an equation of the tangent plane to the given surface at the specified point.

Find an equation of the tangent plane to the given surface at the specified point. <div style=padding-top: 35px>

Question

Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)

A) 6.91

<strong>Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)</strong> A) 6.91 B) 6.99 C) D) 8.34 E) 6.7 <div style=padding-top: 35px>

B) 6.99

<strong>Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)</strong> A) 6.91 B) 6.99 C) D) 8.34 E) 6.7 <div style=padding-top: 35px>

C)

<strong>Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)</strong> A) 6.91 B) 6.99 C) D) 8.34 E) 6.7 <div style=padding-top: 35px>

<strong>Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)</strong> A) 6.91 B) 6.99 C) D) 8.34 E) 6.7 <div style=padding-top: 35px>

D) 8.34

<strong>Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)</strong> A) 6.91 B) 6.99 C) D) 8.34 E) 6.7 <div style=padding-top: 35px>

E) 6.7

<strong>Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)</strong> A) 6.91 B) 6.99 C) D) 8.34 E) 6.7 <div style=padding-top: 35px>

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1/8

Deck 11: Extension D: Partial Derivatives

1

Let

Let and suppose that changes from to (a)Compute (b)Compute

and suppose that Let and suppose that changes from to (a)Compute (b)Compute

Let and suppose that changes from to (a)Compute (b)Compute

changes from Let and suppose that changes from to (a)Compute (b)Compute

Let and suppose that changes from to (a)Compute (b)Compute

to

Let and suppose that changes from to (a)Compute (b)Compute

(a)Compute Let and suppose that changes from to (a)Compute (b)Compute

Let and suppose that changes from to (a)Compute (b)Compute

(b)Compute Let and suppose that changes from to (a)Compute (b)Compute

Let and suppose that changes from to (a)Compute (b)Compute

(a)

(a) (b)

(b)

(a) (b)

2

Find the differential of the function

Find the differential of the function

3

Find the differential of the function

A)

<strong>Find the differential of the function </strong> A) B) C) D)

B)

<strong>Find the differential of the function </strong> A) B) C) D)

C)

<strong>Find the differential of the function </strong> A) B) C) D)

D)

<strong>Find the differential of the function </strong> A) B) C) D)

4

Find the equation of the tangent plane to the given surface at the specified point.

A)

<strong>Find the equation of the tangent plane to the given surface at the specified point. </strong> A) B) C) D) E)

B)

<strong>Find the equation of the tangent plane to the given surface at the specified point. </strong> A) B) C) D) E)

C)

<strong>Find the equation of the tangent plane to the given surface at the specified point. </strong> A) B) C) D) E)

D)

<strong>Find the equation of the tangent plane to the given surface at the specified point. </strong> A) B) C) D) E)

E)

<strong>Find the equation of the tangent plane to the given surface at the specified point. </strong> A) B) C) D) E)

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5

Find the equation of the tangent plane to the given surface at the specified point.

Find the equation of the tangent plane to the given surface at the specified point.

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6

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height cm if the tin is 0.04 cm thick.

cm if the tin is 0.04 cm thick.

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7

Find an equation of the tangent plane to the given surface at the specified point.

Find an equation of the tangent plane to the given surface at the specified point.

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8

Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)

A) 6.91

<strong>Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)</strong> A) 6.91 B) 6.99 C) D) 8.34 E) 6.7

B) 6.99

<strong>Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)</strong> A) 6.91 B) 6.99 C) D) 8.34 E) 6.7

C)

<strong>Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)</strong> A) 6.91 B) 6.99 C) D) 8.34 E) 6.7

<strong>Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)</strong> A) 6.91 B) 6.99 C) D) 8.34 E) 6.7

D) 8.34

<strong>Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)</strong> A) 6.91 B) 6.99 C) D) 8.34 E) 6.7

E) 6.7

<strong>Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)</strong> A) 6.91 B) 6.99 C) D) 8.34 E) 6.7

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