Answer this question. Part (4), (5) & (6). Derivative of a function f(t)with respect to r is the measure of how fast the function is changingwith respect to 1. Mathematically the derivative at a point is defined asf (1) = limf) > 0, the function is increasing with respect to 1, similarly if f (t) < 0 the function isdecreasing with respect to t.h-0According to the standard results, the derivative of the " is 4" = nt-1, where n is an integer.If a is a constant, then derivative of function in the form af(1) is 4 (af(t) = af (t).The equation for magnetic field that developed under the presence of magnetic field is givenby v(1) = 0. 250r* + 0. 166r² – 0. 500r². To find a mathematical model for the voltage rate,differentiate the function v(t) with respect to time. Use the result 4 = nt"-l to simplify theexpression.vr(t)= (0. 250r* + 0. 166r° – 0. 500/')=0. 250r + 0. 1664 – 0. 5004=0. 250 - 41 + 0. 166 - 31 – 0. 500 - 21=1.000 + 0. 49872 – 1.000t Analysis 2: The voltage potential, v(t), builds up on the loops, based on the orientation of the magneticfield during an MR scan is given by:v(t) = 0.250t+ + 0.166t³ – 0.500and the voltage at time t= 0 is 0.1. Formulate the mathematical model for the voltage rate vr(t) developed at the loops duringscanning.2. Plot/Sketch vr(t) as a function of time t E [-4 : 4].3. Find the roots of vr(t) analytically.4. Use your figure to study the sign of vr(t) in the time interval [-4 : 4]. Does vr(t) have any root in theinterval [-4 : 4]? If yes, estimate the roots graphically.5. Manually use Bisection iterative technique with 6 iterations to find a root of vr(t) in the intervals[0.3 : 0.7] and [-1 :-5]. Calculate the percentage of error. Show details of your steps.6. Manually use Newton-Raphson iterative technique with 6 iterations to find a root of vr(t) in theintervals [0.3 : 0.7] and [-1 : -5]. Calculate the percentage of error. Show details of your steps.

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Description: Answer this question. Part (4), (5) & (6). Derivative of a function f(t)with respect to r is the measure of how fast the function is changingwith respect to 1. Mathematically the derivative at a point is defined asf (1) = limf) > 0, the function is i

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Analysis 2: The voltage potential, v(t), builds up on the loops, based on the orientation of the magnetic field during an MR scan is given by: v(t) = 0.250t+ + 0.166t3 – 0.500r and the voltage at time t= 0 is 0. 1. Formulate the mathematical model for the voltage rate vr(t) developed at the loops during scanning. 2. Plot/Sketch vr(t) as a function of time t E [-4 : 4]. 3. Find the roots of vr(t) analytically. 4. Use your figure to study the sign of vr(t) in the time interval [-4 : 4]. Does vr(t) have any root in the interval [-4 : 4]? If yes, estimate the roots graphically. 5. Manually use Bisection iterative technique with 6 iterations to find a root of vr(t) in the intervals [0.3 : 0.7] and [-1 :-5]. Calculate the percentage of error. Show details of your steps. 6. Manually use Newton-Raphson iterative technique with 6 iterations to find a root of vr(t) in the intervals [0.3 : 0.7] and [-1 : -5]. Calculate the percentage of error. Show details of your steps.

Analysis 2: The voltage potential, v(t), builds up on the loops, based on the orientation of the magnetic field during an MR scan is given by: v(t) = 0.250t+ + 0.166t3 – 0.500r and the voltage at time t= 0 is 0. 1. Formulate the mathematical model for the voltage rate vr(t) developed at the loops during scanning. 2. Plot/Sketch vr(t) as a function of time t E [-4 : 4]. 3. Find the roots of vr(t) analytically. 4. Use your figure to study the sign of vr(t) in the time interval [-4 : 4]. Does vr(t) have any root in the interval [-4 : 4]? If yes, estimate the roots graphically. 5. Manually use Bisection iterative technique with 6 iterations to find a root of vr(t) in the intervals [0.3 : 0.7] and [-1 :-5]. Calculate the percentage of error. Show details of your steps. 6. Manually use Newton-Raphson iterative technique with 6 iterations to find a root of vr(t) in the intervals [0.3 : 0.7] and [-1 : -5]. Calculate the percentage of error. Show details of your steps.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Answer this question. Part (4), (5) & (6).

Derivative of a function f(t)with respect to r is the measure of how fast the function is changing
with respect to 1. Mathematically the derivative at a point is defined asf (1) = lim
f) > 0, the function is increasing with respect to 1, similarly if f (t) < 0 the function is
decreasing with respect to t.
h-0
According to the standard results, the derivative of the " is 4" = nt-1, where n is an integer.
If a is a constant, then derivative of function in the form af(1) is 4 (af(t) = af (t).
The equation for magnetic field that developed under the presence of magnetic field is given
by v(1) = 0. 250r* + 0. 166r² – 0. 500r². To find a mathematical model for the voltage rate,
differentiate the function v(t) with respect to time. Use the result 4 = nt"-l to simplify the
expression.
vr(t)= (0. 250r* + 0. 166r° – 0. 500/')
=0. 250r + 0. 1664 – 0. 5004
=0. 250 - 41 + 0. 166 - 31 – 0. 500 - 21
=1.000 + 0. 49872 – 1.000t

Analysis 2: The voltage potential, v(t), builds up on the loops, based on the orientation of the magnetic
field during an MR scan is given by:
v(t) = 0.250t+ + 0.166t³ – 0.500
and the voltage at time t= 0 is 0.
1. Formulate the mathematical model for the voltage rate vr(t) developed at the loops during
scanning.
2. Plot/Sketch vr(t) as a function of time t E [-4 : 4].
3. Find the roots of vr(t) analytically.
4. Use your figure to study the sign of vr(t) in the time interval [-4 : 4]. Does vr(t) have any root in the
interval [-4 : 4]? If yes, estimate the roots graphically.
5. Manually use Bisection iterative technique with 6 iterations to find a root of vr(t) in the intervals
[0.3 : 0.7] and [-1 :-5]. Calculate the percentage of error. Show details of your steps.
6. Manually use Newton-Raphson iterative technique with 6 iterations to find a root of vr(t) in the
intervals [0.3 : 0.7] and [-1 : -5]. Calculate the percentage of error. Show details of your steps.

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