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(3 points) The figure shows how a function f (x) and its linear approximation (.e., its...
The function f(x) changes value when x changes from xo to xo + dx. Find the...
The function f(x) changes value when x changes from xo to xo + dx. Find the change Af=f(xo + dx) = f(xo), the value of the estimate df = f'(x) dx, and the approximation error Af - dfſ. f(x) = 9x2 + 7%, * = 1, dx = 0.1 y = 0 T (T Af + d) - Mr) de ful Tangent 0 lue of Δf = (Type an integer or a decimal. Do not round.) df = 0 (Type...
Assigned Each function f(x) changes value when x changes from Xo to xo + dx. Find...
Assigned Each function f(x) changes value when x changes from Xo to xo + dx. Find the change Af = f(xo + dx) – f(xo), the value of the estimate df = f'(xo) dx, and the approximate error Af-df| f(x) = 4x2 - 5x, Xo = 2, dx = 0.1 The change Af=0. (Simplify your answer. Type an integer or a y=f Af = f + de) - doda of)) de Tangent о + de
6. Linear Approximation a. Suppose you have a function f(x), and suppose you know df|3 =...
6. Linear Approximation a. Suppose you have a function f(x), and suppose you know df|3 = −4 dx. What is the equation of the tangent line to y = f(x) at x = 3, if f(3) = 7? And give an estimate of f(2.8). b. The volume of a sphere of radius r is V = 1 3 πr3 . Find dV in terms of dr. Then find dV V in terms of dr r , and use it to...
T3-EOY-MAT70 10- Choose the correct answer Hint on steps to follow: Find f'(x) or df/dx Then...
T3-EOY-MAT70 10- Choose the correct answer Hint on steps to follow: Find f'(x) or df/dx Then f'(x) Then f(x) (the given integral with upper limit as xo) Then plug in the equation of the tangent: y -f(x) = f'(x)=(x-x) • Simplify it. Given f(x) = Se' dt. Find the equation of the tangent line to f(x) at x = 2 y = e-2x - e? – 1 y=e-2x - 1
Each function f(x) changes value when x changes from x0 to x0 + dx. Find the change Δ.fX0 + dx)-foo), the value of the...
Each function f(x) changes value when x changes from x0 to x0 + dx. Find the change Δ.fX0 + dx)-foo), the value of the estimate df- The change Δ-1.902 (Round to the nearest thousandth.) r (%) d, and the approximate error la-dfl. The value of the estimate df f(x)-6x-4, X,--1.1 , dx=0.1 (Round to the nearest thousandth.) dx Tangent 0 to
Each function f(x) changes value when x changes from x0 to x0 + dx. Find the change Δ.fX0 +...
4. Given a function f(x), use Taylor approximations to derive a second order one-sided ap- proximation to f'(ro...
4. Given a function f(x), use Taylor approximations to derive a second order one-sided ap- proximation to f'(ro) is given by f(zo + h) + cf (zo + 21) + 0(h2). f' (zo) = af(xo) + What is the precise form of the error term? Using the formula approximate f' (1) where r) = e* for h 1/(2p) for p = 1 : 15, Form a table with columns giving h, the approximation, absolute error and absolute error divided by...
2. Suppose the linear approximation of a differentiable function f(x, y, z) at the point (1,2,3)...
2. Suppose the linear approximation of a differentiable function f(x, y, z) at the point (1,2,3) is given by L(x, y, z) = 17+ 6(x – 1) – 4(y – 2) + 5(2 – 3). Suppose furthermore that x, y and z are functions of (s, t), with (x(0,0), y(0,0), z(0,0)) = (1, 2, 3), and the differentials computed at (s, t) = (0,0) are given by dx = 7ds + 10dt, dy = 4ds – 3dt, dz = 2ds...
At least one of the answers above is NOT correct. (1 point) Suppose f(x, t) =...
At least one of the answers above is NOT correct. (1 point) Suppose f(x, t) = e 3t sin(x + 2t). (a) At any point (x, t), the differential is df = e^(-3t)cos(x+2t)dx+(e^(-3t))(2cos(x+2t)-2sin(x+2t))dt (b) At the point (-1,0), the differential is df = cos(-1)dx+(2cos(-1))+3sin(-1)dt (c) At the point (-1,0) with dx = -0.5 and dt = 0.3, the differential is df = 0.97344 Note. You can earn partial credit on this nrohlem (1 point) Consider the surface xyz = 20....
7. (5 points) Find the linear approximation for f(x) = tan(2x) at a = 0 and...
7. (5 points) Find the linear approximation for f(x) = tan(2x) at a = 0 and use it to approximate the value of tan(0.002). Hint: The linear approximation is just the tangent line to the curve at a = 2. 8. (5 points) Use the Mean Value Theorem for derivatives to find the value of x = c for f(x) = Vx on the interval (1,9). 9. (5 points) The acceleration of an object moving along the number line at...
1. Linear Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ = 0.4, Comput...
1. Linear Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ = 0.4, Compute the relative error: Then compare f(x) and L(x) LLarrul × 100% 1f(x)1 r(x)l
1. Linear Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ...
The function f(x) changes value when x changes from xo to xo + dx. Find the change Af=f(xo + dx) = f(xo), the value of the estimate df = f'(x) dx, and the approximation error Af - dfſ. f(x) = 9x2 + 7%, * = 1, dx = 0.1 y = 0 T (T Af + d) - Mr) de ful Tangent 0 lue of Δf = (Type an integer or a decimal. Do not round.) df = 0 (Type...
Assigned Each function f(x) changes value when x changes from Xo to xo + dx. Find the change Af = f(xo + dx) – f(xo), the value of the estimate df = f'(xo) dx, and the approximate error Af-df| f(x) = 4x2 - 5x, Xo = 2, dx = 0.1 The change Af=0. (Simplify your answer. Type an integer or a y=f Af = f + de) - doda of)) de Tangent о + de
T3-EOY-MAT70 10- Choose the correct answer Hint on steps to follow: Find f'(x) or df/dx Then f'(x) Then f(x) (the given integral with upper limit as xo) Then plug in the equation of the tangent: y -f(x) = f'(x)=(x-x) • Simplify it. Given f(x) = Se' dt. Find the equation of the tangent line to f(x) at x = 2 y = e-2x - e? – 1 y=e-2x - 1
Each function f(x) changes value when x changes from x0 to x0 + dx. Find the change Δ.fX0 + dx)-foo), the value of the estimate df- The change Δ-1.902 (Round to the nearest thousandth.) r (%) d, and the approximate error la-dfl. The value of the estimate df f(x)-6x-4, X,--1.1 , dx=0.1 (Round to the nearest thousandth.) dx Tangent 0 to
Each function f(x) changes value when x changes from x0 to x0 + dx. Find the change Δ.fX0 +...
4. Given a function f(x), use Taylor approximations to derive a second order one-sided ap- proximation to f'(ro) is given by f(zo + h) + cf (zo + 21) + 0(h2). f' (zo) = af(xo) + What is the precise form of the error term? Using the formula approximate f' (1) where r) = e* for h 1/(2p) for p = 1 : 15, Form a table with columns giving h, the approximation, absolute error and absolute error divided by...
2. Suppose the linear approximation of a differentiable function f(x, y, z) at the point (1,2,3) is given by L(x, y, z) = 17+ 6(x – 1) – 4(y – 2) + 5(2 – 3). Suppose furthermore that x, y and z are functions of (s, t), with (x(0,0), y(0,0), z(0,0)) = (1, 2, 3), and the differentials computed at (s, t) = (0,0) are given by dx = 7ds + 10dt, dy = 4ds – 3dt, dz = 2ds...
At least one of the answers above is NOT correct. (1 point) Suppose f(x, t) = e 3t sin(x + 2t). (a) At any point (x, t), the differential is df = e^(-3t)cos(x+2t)dx+(e^(-3t))(2cos(x+2t)-2sin(x+2t))dt (b) At the point (-1,0), the differential is df = cos(-1)dx+(2cos(-1))+3sin(-1)dt (c) At the point (-1,0) with dx = -0.5 and dt = 0.3, the differential is df = 0.97344 Note. You can earn partial credit on this nrohlem (1 point) Consider the surface xyz = 20....
7. (5 points) Find the linear approximation for f(x) = tan(2x) at a = 0 and use it to approximate the value of tan(0.002). Hint: The linear approximation is just the tangent line to the curve at a = 2. 8. (5 points) Use the Mean Value Theorem for derivatives to find the value of x = c for f(x) = Vx on the interval (1,9). 9. (5 points) The acceleration of an object moving along the number line at...
1. Linear Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ = 0.4, Compute the relative error: Then compare f(x) and L(x) LLarrul × 100% 1f(x)1 r(x)l
1. Linear Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ...
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