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Use technology to draw a slope field for the differential equation y' = 2y3 - 50y. Sketch the solutions that satisfy the initial condition y(0) = c for various values of c. For what values of c does the limit L = lim y(t) exist? ○ CE [0, 5] t→ ∞ ○ CE [-5,0] O CE [-5, 5] Oc€ (-∞, -5] ○ c€ [5,∞) What are the possible values for this limit L? (Enter your answers as a comma-separated list.) L = Consider the following function. f(x) = x 4/7, a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = 1 + (x- 1) 6 49 (x-1)² + 20 343 (x-1)3 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) = (x) when x lies in the given interval. (Round your answer to eight decimal places.) R3(x) 0.0000896 X (c) Check your result in part (b) by graphing |R(x). -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 0.00010 0.00008 0.00006 0.00004 0.00002 y x 0.9 1.1 1.2 -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 0.9 1.0 1.1 1.2 y 0.00010 0.00008 0.00006 0.00004 0.00002 y x 1.0 1.1 1.2 x 0.9 1.0 1.1 1.2

Use technology to draw a slope field for the differential equation y' = 2y3 - 50y. Sketch the solutions that satisfy the initial condition y(0) = c for various values of c. For what values of c does the limit L = lim y(t) exist? ○ CE [0, 5] t→ ∞ ○ CE [-5,0] O CE [-5, 5] Oc€ (-∞, -5] ○ c€ [5,∞) What are the possible values for this limit L? (Enter your answers as a comma-separated list.) L = Consider the following function. f(x) = x 4/7, a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = 1 + (x- 1) 6 49 (x-1)² + 20 343 (x-1)3 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) = (x) when x lies in the given interval. (Round your answer to eight decimal places.) R3(x) 0.0000896 X (c) Check your result in part (b) by graphing |R(x). -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 0.00010 0.00008 0.00006 0.00004 0.00002 y x 0.9 1.1 1.2 -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 0.9 1.0 1.1 1.2 y 0.00010 0.00008 0.00006 0.00004 0.00002 y x 1.0 1.1 1.2 x 0.9 1.0 1.1 1.2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 51E
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Use technology to draw a slope field for the differential equation y' = 2y3 - 50y. Sketch the solutions that satisfy the initial condition y(0) = c for various values of c. For what values of c does the limit L = lim y(t) exist? ○ CE [0, 5] t→ ∞ ○ CE [-5,0] O CE [-5, 5] Oc€ (-∞, -5] ○ c€ [5,∞) What are the possible values for this limit L? (Enter your answers as a comma-separated list.) L =
Transcribed Image Text:Use technology to draw a slope field for the differential equation y' = 2y3 - 50y. Sketch the solutions that satisfy the initial condition y(0) = c for various values of c. For what values of c does the limit L = lim y(t) exist? ○ CE [0, 5] t→ ∞ ○ CE [-5,0] O CE [-5, 5] Oc€ (-∞, -5] ○ c€ [5,∞) What are the possible values for this limit L? (Enter your answers as a comma-separated list.) L =
Consider the following function. f(x) = x 4/7, a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = 1 + (x- 1) 6 49 (x-1)² + 20 343 (x-1)3 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) = (x) when x lies in the given interval. (Round your answer to eight decimal places.) R3(x) 0.0000896 X (c) Check your result in part (b) by graphing |R(x). -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 0.00010 0.00008 0.00006 0.00004 0.00002 y x 0.9 1.1 1.2 -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 0.9 1.0 1.1 1.2 y 0.00010 0.00008 0.00006 0.00004 0.00002 y x 1.0 1.1 1.2 x 0.9 1.0 1.1 1.2
Transcribed Image Text:Consider the following function. f(x) = x 4/7, a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = 1 + (x- 1) 6 49 (x-1)² + 20 343 (x-1)3 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) = (x) when x lies in the given interval. (Round your answer to eight decimal places.) R3(x) 0.0000896 X (c) Check your result in part (b) by graphing |R(x). -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 0.00010 0.00008 0.00006 0.00004 0.00002 y x 0.9 1.1 1.2 -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 0.9 1.0 1.1 1.2 y 0.00010 0.00008 0.00006 0.00004 0.00002 y x 1.0 1.1 1.2 x 0.9 1.0 1.1 1.2
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