3. The radius of a large sphere is increasing at the rate of 8m/ sec. At what rate is the sphere changing surface area when the radius of the sphere is 12m. Solution:
3. The radius of a large sphere is increasing at the rate of 8m/ sec. At what rate is the sphere changing surface area when the radius of the sphere is 12m. Solution:
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![3. The radius of a large sphere is increasing at the rate of 8m / sec. At what rate is the sphere
changing surface area when the radius
the sphere is 12 m .
Solution:
dy
- by using logarithmic differentiation for the function y=lnxrnx
dx
4. Find
Solution:
5. Solve the initial value problem f'(x) = 3x² + 2x – 5 , f(1) = 2
Solution:
6. Consider the function f(x) = x' +x² -8x +3. Using second derivative test , determine whether
f has a local maximum or local minimum at those points.
Solution:
1
3
dx
2x?
7. Evaluate
r +--
Solution:
8. For the function f(x)=x³ – 6x² + 9x – 5 , determine
i) intervals where f is increasing or decreasing
ii) local minima and maxima of f
iii) intervals where f is concave up and concave down.
iv) The inflection point of f
Solution:
9. Find the equation of the normal to the tangent line for the equation x’y+ xy² +x² + y² = 0 at the
point (-1,1) .
Solution:
10. Verify the Rolle's theorem for the function ƒ (x)=- x² + 6x – 6 in [1,5].
Solution:
2 csc? x
11. Evaluate |
dx by using substitution method.
(1– cot x)'
Page 3 of 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6562abec-fd5b-4654-97e8-c4530eab1de4%2Fb11fb57c-f595-4fe9-92a9-db2a3724da65%2Fvg06nq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. The radius of a large sphere is increasing at the rate of 8m / sec. At what rate is the sphere
changing surface area when the radius
the sphere is 12 m .
Solution:
dy
- by using logarithmic differentiation for the function y=lnxrnx
dx
4. Find
Solution:
5. Solve the initial value problem f'(x) = 3x² + 2x – 5 , f(1) = 2
Solution:
6. Consider the function f(x) = x' +x² -8x +3. Using second derivative test , determine whether
f has a local maximum or local minimum at those points.
Solution:
1
3
dx
2x?
7. Evaluate
r +--
Solution:
8. For the function f(x)=x³ – 6x² + 9x – 5 , determine
i) intervals where f is increasing or decreasing
ii) local minima and maxima of f
iii) intervals where f is concave up and concave down.
iv) The inflection point of f
Solution:
9. Find the equation of the normal to the tangent line for the equation x’y+ xy² +x² + y² = 0 at the
point (-1,1) .
Solution:
10. Verify the Rolle's theorem for the function ƒ (x)=- x² + 6x – 6 in [1,5].
Solution:
2 csc? x
11. Evaluate |
dx by using substitution method.
(1– cot x)'
Page 3 of 4
![Solution:
12. Verify the Mean Value theorem for the function f(x)= x* – x² +1 on [-1,1]
Solution:
13. Evaluate [(4x +2)vx² +x + ldx by using substitution method.
Solution:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6562abec-fd5b-4654-97e8-c4530eab1de4%2Fb11fb57c-f595-4fe9-92a9-db2a3724da65%2Fljrdnrc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solution:
12. Verify the Mean Value theorem for the function f(x)= x* – x² +1 on [-1,1]
Solution:
13. Evaluate [(4x +2)vx² +x + ldx by using substitution method.
Solution:
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning