
Concept explainers
(a)
To find:
An equation of the tangent plane at the point
Solution:
Explanation:
1) Concept:
The equation of the tangent plane is
Where
2) Given:
The parametric surface
3) Calculations:
The parametric surface
To find the tangent vectors
The normal vector to the tangent plane is
This can be written as,
At the point
For
The position vector of a point
The equation of the tangent plane is
This is the equation of the tangent plane
Conclusion:
Thus, anequation of the tangent plane at the point
(b)
To draw:
The graph of surface
Solution:
Explanation:
1) Concept:
To draw the graph of surface
2) Calculations:
The parametric surface
The equation of the tangent plane is
To draw the graph of surface
Conclusion:
The graph of surface
(c)
To set up:
An integral for the surface area
Solution:
Explanation:
1) Concept:
If a smooth parametric surface
And
Where
2) Given:
The parametric surface
3) Calculations:
The parametric surface
The surface area
Conclusion:
An integral for the surface area
(d)
To find:
Solution:
Explanation:
1) Concept:
2) Given:
3) Calculations:
From the part (a),
The surface integral is,
To find
Substitute this value insurface integral
Use the command in Mathematica
Therefore,
Conclusion:

Want to see the full answer?
Check out a sample textbook solution
Chapter 16 Solutions
Calculus (MindTap Course List)
- i don't understand how to get these answers please help!arrow_forwardEnter your answer in interval notation. No decimal entries allowed. Type oo (lower case o) for ∞ and -oo for -∞ if needed. Domain: Question Help: Message instructorarrow_forwardWrite a formula for the function g that results when the graph of the function f(x) = = 4 X is reflected about the y-axis, horizontally compressed by a factor of 2, shifted 7 units left, reflected about the x-axis and shifted 3 units up. g(x): = Question Help: Message instructorarrow_forward
- Question 7 4 pts 1 Details The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x) = 1.8208e0.3387x, where x = 0 corresponds to 1998. In what year did/will the exports reach $10.4 billion?arrow_forwardQuestion 7 4 pts 1 Detai The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x) = 1.8208e 0.3387x, where x = 0 corresponds to 1998. In what year did/will the exports reach $10.4 billion?arrow_forwardWrite a formula for the function g that results when the graph of the function f(x) = = 4 X is reflected about the y-axis, horizontally compressed by a factor of 2, shifted 7 units left, reflected about the x-axis and shifted 3 units up. g(x) = Question Help: Message instructorarrow_forward
- Question 3 Use the graph of f to evaluate the following: 3 pts 1 D 6 f(x) 5 4 3 2 1 -1 1 2 3 4 5 เค -1 x The average rate of change of f from 1 to 4 =arrow_forwardB Find the domain the function graphed below. Express in interval notation 5 3 pts 1 De 3 2 1 -5 -4 -3 2 -1 2 3 4 5 -2 -3 -4 5 Domain:arrow_forwardFind the domain the function graphed below. Express in interval notation 3 2 -5 4-3 12 -1 1 2 3 4 2 -3- 4 5+ Domain: Question Help: Message instructor Question 3arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
