Use technology to draw a slope field for the differential equation y' = 2y3 - 50y. Sketch the solutions that satisfy the initialcondition 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)649(x-1)² +20343(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. (Roundyour answer to eight decimal places.)R3(x) 0.0000896 X(c) Check your result in part (b) by graphing |R(x).-0.00002-0.00004-0.00006-0.00008-0.000100.000100.000080.000060.000040.00002yx0.91.11.2-0.00002-0.00004-0.00006-0.00008-0.000100.91.01.11.2y0.000100.000080.000060.000040.00002yx1.01.11.2x0.91.01.11.2

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Answered: Use technology to draw a slope field…

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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If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f decreases on the interval -,x1 and increases on the interval x1,, then fx1 is a local maximum value.
Use Taylor's polynomial of degree 2 of the function f(x) = tan (x+1) + x² about c = - 1 to estimate the value of f (- 0.7). Enter a decimal such as as 1.04, -2.573, -0.023 , 0.15 , etc. No spaces please and no rounding!
Consider the following function. f(x) = x6/7, a = 1, n = 3, (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) = T(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R3(x)| Enter a number. (c) Check your result in part (b) by graphing IR (X). -5.x 10 -6 y -0.000010 -0.000015 -0.000020 -0.000025 -0.000030 -0.000035 y 0.000035 0.000030 0.000025 0.000020 0.000015 0.000010 5.x 10 -6 0.9 0.9 0.8 ≤ x ≤ 1.2 1.0 1.0 1.1 1.1 1.2 1.2 X X 0.000035 0.000030 0.000025 0.000020 0.000015 0.000010 y -6 5.x 10 -5.x 10 y -6 -0.000010 -0.000015 -0.000020 -0.000025 -0.000030 -0.000035 0.9 0.9 1.0 1.1 1.1 X 1.2 1.2 X
[3.1]
Consider the following function. f(x)=²x², a = 0, n=3, 0 ≤x≤0.1 (a) Approximate f by a Taylor polynomial with degreen at the number a. T₂(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) T(x) when x lies in the given interval. (Round your answer to five decimal places.) IR₂(x)| ≤[
Consider the following function. f(x) = x6/7, a = 1, n = 3, 0.7 ≤ x ≤ 1.3. (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) T(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R3(x)| ≤ (c) Check your result in part (b) by graphing IR,(x). y 0.00015 0.00010 0.00005 X 0.8 0.9 1.0 1.1 1.2 1.3 y -0.00005 -0.00010 -0.00015 O X 08 0.9 1.0 1.1 1.2 1.3 y -0.00005 -0.00010 -0.00015 0.8 0.9 11.0 1.1 1.2 1.3 X y 0.00015 ELV 0.00010 0.00005 X 0.8 0.9 1.0 1.1 1.2 1.3
Find the Taylor polynomial T,(x) for the function f(x) = 3e* at x 0, (Use symbolic notation and fractions where needed.) T2(x) = Use a calculator to compute the error at x = -0.5. (Use decimal notation. Give your answer to three decimal places.) I/) - T;(x)|
6. Consider the function f(x) 1 , x > 0. x + 2 (a) Find the interpolating polynomial P2(x) that agrees with f at the points x1 = 0, x2 = 1, xz = 2. (You may use Lagrange's interpolation formula or Newton's divided differences formula). (b) Use the above polynomial P2(x) to approximate f(1.5). (c) Find an upper bound for the error |f(1.5) – P2(1.5)| using the appropriate error formula and compare your result with the actual error.
Consider the following function. f(x) = x¹/3, a = 1, n = 3, (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x)= T(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R3(x)| ≤ (c) Check your result in part (b) by graphing IR,(x)|. y 0.00012 0.00010 0.00008 0.00006 0.00004 0.00002 y -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 -0.00012 0.9 0.9 0.8 ≤ x ≤ 1.2 1.0 1.0 1.1 1.1 1.2 1.2 X X y 0.00012 0.00010 0.00008 0.00006 0.00004 0.00002 y -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 0.00012 0.9 0.9 1.0 1.1 1.1 1.2 1.2 X
Consider the following function. f (x) = x/3, a = 1, n = 3,0.8

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