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Find the sensitivity of y = f(x) at the point specified in Problems 13 to 18, and use it to estimate Ay for the given measurement error Ax. 13. y = Vx at x = 9, with Ar = 0.01 14. y = v2x2+1 at x = -2, with Ax = 0.01 15. y = In x at x = 2, with Ax = -0.2 16. y = cot x at x = with Ax 0.1 2' 17. y = cos x at x = with Ax = -0.01 2' %3D 1 at x = 0, with Ax = -0.05 x +1 18. y = %3D

Find the sensitivity of y = f(x) at the point specified in Problems 13 to 18, and use it to estimate Ay for the given measurement error Ax. 13. y = Vx at x = 9, with Ar = 0.01 14. y = v2x2+1 at x = -2, with Ax = 0.01 15. y = In x at x = 2, with Ax = -0.2 16. y = cot x at x = with Ax 0.1 2' 17. y = cos x at x = with Ax = -0.01 2' %3D 1 at x = 0, with Ax = -0.05 x +1 18. y = %3D

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.2: Power Functions
Problem 17E: Tsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height...
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Note that this answer does not depend on w or h but is a pure number! Think about why this is the case. b. Since the elasticity is -2, an x% error in h results in a –2x% error in our estimate for BMI. To ensure that our error is no greater than ±5%, we need to ensure that the error in the measurement of the height is no greater than +2.5%. PROBLEM SET 3.5 Level 1 DRILL PROBLEMS Find the sensitivity of y Problems 13 to 18, and use it to estimate Ay for the given f(x) at the point specified in In Problems 1 to 6 find the linear approximation of y = f(x) at the specified point, and use technology to graph the function and its linear approximation to deter- mine whether the linear approximation tends to overesti- mate or underestimate y = f(x) near the specified point. measurement error Ax. 13. у — Vx at x = 9, with Ax = 0.01 14. y = V2x2 +1 at x = -2, with Ax = 0.01 15. y = In x at x = 2, with Ax = –0.2 IT 1. y = coS x at x = 2 IT with Ax = 0.1 2' 2. у — е* at х — 0. 16. У = cot x at x = IT with Ax = 2 3. У sin x at x = 2 4. y = x² at x = -2 17. y = = COS x at x = -0.01 1 at x = 2 1 at x = 0, with Ax = -0.05 x +1 5. У 6. у %3 хе * atx 3 In 2 18. y = 1+x² In Problems 7 to 12, estimate the indicated quantity using a linear approximation around the given point x and compare to the true value obtained using technology. Find the elasticity of y = f(x) at the point specified in Problems 19 to 24 and use it to estimate the percent error in y for the given percent error in x. 19. у Vx at x = 9, with 1% error in x 7. /26, x = 25 8. V0.99, x =1 20. y = /2x2 +1 at x = -2, with 8% error in x «(플 +001). IT X = IT 9. In 0.9, x =1 10. cos + 0.0 21. y = In x at x = 2, with 5% error in x IT with 10% error in x 2 22. y = = cot x at x 11. tan 0.2, x = 0 12. е -0.2 ', x = 0
Transcribed Image Text:Note that this answer does not depend on w or h but is a pure number! Think about why this is the case. b. Since the elasticity is -2, an x% error in h results in a –2x% error in our estimate for BMI. To ensure that our error is no greater than ±5%, we need to ensure that the error in the measurement of the height is no greater than +2.5%. PROBLEM SET 3.5 Level 1 DRILL PROBLEMS Find the sensitivity of y Problems 13 to 18, and use it to estimate Ay for the given f(x) at the point specified in In Problems 1 to 6 find the linear approximation of y = f(x) at the specified point, and use technology to graph the function and its linear approximation to deter- mine whether the linear approximation tends to overesti- mate or underestimate y = f(x) near the specified point. measurement error Ax. 13. у — Vx at x = 9, with Ax = 0.01 14. y = V2x2 +1 at x = -2, with Ax = 0.01 15. y = In x at x = 2, with Ax = –0.2 IT 1. y = coS x at x = 2 IT with Ax = 0.1 2' 2. у — е* at х — 0. 16. У = cot x at x = IT with Ax = 2 3. У sin x at x = 2 4. y = x² at x = -2 17. y = = COS x at x = -0.01 1 at x = 2 1 at x = 0, with Ax = -0.05 x +1 5. У 6. у %3 хе * atx 3 In 2 18. y = 1+x² In Problems 7 to 12, estimate the indicated quantity using a linear approximation around the given point x and compare to the true value obtained using technology. Find the elasticity of y = f(x) at the point specified in Problems 19 to 24 and use it to estimate the percent error in y for the given percent error in x. 19. у Vx at x = 9, with 1% error in x 7. /26, x = 25 8. V0.99, x =1 20. y = /2x2 +1 at x = -2, with 8% error in x «(플 +001). IT X = IT 9. In 0.9, x =1 10. cos + 0.0 21. y = In x at x = 2, with 5% error in x IT with 10% error in x 2 22. y = = cot x at x 11. tan 0.2, x = 0 12. е -0.2 ', x = 0
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