a.
Find approximation error of the function.
a.
Answer to Problem 101E
Explanation of Solution
Given information:
Use the polynomial approximations of the sine and cosine functions in Exercise 100 to approximate the following function values. Compare the results with those given by a calculator. Is the error in the approximation the same in each case? Explain.
Calculation:
Approximation of sine function by polynomials is,
Using approximation above, for
Using graphic calculator, you get
Hence, approximation error is
b.
Find approximation error of the function.
b.
Answer to Problem 101E
Explanation of Solution
Given information:
Use the polynomial approximations of the sine and cosine functions in Exercise 100 to approximate the following function values. Compare the results with those given by a calculator. Is the error in the approximation the same in each case? Explain.
Calculation:
Approximation of sine function by polynomials is,
Using approximation above, for
Using graphic calculator, you get
Hence, approximation error is
c.
Find approximation error of the function.
c.
Answer to Problem 101E
Explanation of Solution
Given information:
Use the polynomial approximations of the sine and cosine functions in Exercise 100 to approximate the following function values. Compare the results with those given by a calculator. Is the error in the approximation the same in each case? Explain.
Calculation:
Approximation of sine function by polynomials is,
Using approximation above, for
Using graphic calculator, you get
Hence, approximation error is
d.
Find approximation error of the function.
d.
Answer to Problem 101E
Explanation of Solution
Given information:
Use the polynomial approximations of the sine and cosine functions in Exercise 100 to approximate the following function values. Compare the results with those given by a calculator. Is the error in the approximation the same in each case? Explain.
Calculation:
Approximation of cosine function by polynomials is,
Using approximation above, for
Using graphic calculator, you get
Hence, approximation error is
e.
Find approximation error of the function.
e.
Answer to Problem 101E
Explanation of Solution
Given information:
Use the polynomial approximations of the sine and cosine functions in Exercise 100 to approximate the following function values. Compare the results with those given by a calculator. Is the error in the approximation the same in each case? Explain.
Calculation:
Approximation of cosine function by polynomials is,
Using approximation above, for
Using graphic calculator, you get
Hence, approximation error is
f.
Find approximation error of the function.
f.
Answer to Problem 101E
Explanation of Solution
Given information:
Use the polynomial approximations of the sine and cosine functions in Exercise 100 to approximate the following function values. Compare the results with those given by a calculator. Is the error in the approximation the same in each case? Explain.
Calculation:
Approximation of cosine function by polynomials is,
Using approximation above, for
Using graphic calculator, you get
Approximation error is
Hence , approximation errors are not same in each case.
Chapter 4 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning