Consider the equation sin x = x2 − x. Explain why there must be a number...
Consider the equation
sin x = x2 − x.
Explain why there must be a number x ∗ ∈ (1.59, 1.63) such that this equation is true. (You should state clearly any properties, results or theorems that you rely on.) Use the interval bisection method to find this number to an accuracy of two decimal places
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Consider the equation
sin x = x2 − x.
Explain why there must be a number...
QUESTION 1 = = (a) Apart from x = 0 the equation f(x) 22 – 4...
QUESTION 1 = = (a) Apart from x = 0 the equation f(x) 22 – 4 sin r 0 has another root in (1, 2.5). Perform three iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x(0) = 1.5 as the initial solution. Compare the error from the Newton's approximation with that incurred for the same...
this is numerical analysis QUESTION 1 (a) Apart from 1 = 0 the equation f(1) =...
this is numerical analysis
QUESTION 1 (a) Apart from 1 = 0 the equation f(1) = x2 - 4 sin r = 0 has another root in (1, 2.5). Perform three (10) iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x) = 1.5 as the initial (10) solution. Compare the error from the Newton's approximation...
Find the general solution of the given differential equation. x y - y = x2 sin(x)...
Find the general solution of the given differential equation. x y - y = x2 sin(x) y(x) = (No Response) Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) (No Response) Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.) (No Response)
Explain why the differential equation v' (I) – sin(x)+(x) + sin(v(x)) = 0) with initial condition...
Explain why the differential equation v' (I) – sin(x)+(x) + sin(v(x)) = 0) with initial condition (0) = 1 has a unique solution for all times < > 0.
Consider the following function #x)-x2/5, a-1, n-3, 0.7 sxs 1.3 (a) Approximate fby a Taylor poly...
Consider the following function #x)-x2/5, a-1, n-3, 0.7 sxs 1.3 (a) Approximate fby a Taylor polynomial with degree n at the number a T3(x) (b) Use Taylor's Inequality to estimate the accuracy of the approximation x) Tn(x) when x lies in the given interval. (Round your answer to eight decimal places.)
Consider the following function #x)-x2/5, a-1, n-3, 0.7 sxs 1.3 (a) Approximate fby a Taylor polynomial with degree n at the number a T3(x) (b) Use Taylor's Inequality to...
Consider the following differential equation. (x2 − 4) dy dx + 4y = (x + 2)2...
Consider the following differential equation.
(x2 − 4)
dy
dx
+ 4y = (x + 2)2
Consider the following differential equation. dy (x2 - 4) dx + 4y = (x + 2)2 Find the coefficient function P(x) when the given differential equation is written in the standard form dy dx + P(x)y = f(x). 4 P(x) = (x2 – 4) Find the integrating factor for the differential equation. SP(x) dx 1 Find the general solution of the given differential equation....
Consider the function: f (x) = b - sin(x), where bis an arbitrary number. Are roots...
Consider the function: f (x) = b - sin(x), where bis an arbitrary number. Are roots always possible for any value of b? Yes No Consider the function: f (x) = a - tan(x), where a is an arbitrary number. Are roots always possible? True False
explain why newtons method doesnt work for finding the root of the equation x^3-3x+9=0 if the...
explain why newtons method doesnt work for finding the root of the
equation
x^3-3x+9=0
if the initial approximation is chosen to be x1=1
f(x)=x^3-3x+9 -> f'(x)= . if x1=1 then f'(x1)= and the
tangent line ued for approximating x2 is . attempting to find x^2
results in trying to by zero
1. [-/100 Points) DETAILS SCALCETS 4.8.031. MY NOTES Explain why Newton's method doesn't work for finding the root of the equation if the initial approximation is chosen to be...
Hi, need help with some Matlab problems. How would this be entered? 1 (a) Let f(x) sin(x)-cos(x)-1. Calculate f(1) and...
Hi, need help with some Matlab problems. How would this be
entered?
1 (a) Let f(x) sin(x)-cos(x)-1. Calculate f(1) and f(2) and then explain why there is an [1.2] such that f(a)--0. You should give your values off to four significant decimal digits. (b) With a andb 2, the first two iterations of the bisection method for the function given in part (a) are shown in the following table. Do two more iterations to find the missing values in the...
The equation f(x) = (1 ‐ x) cos x ‐ sin x = 0 has at...
The equation f(x) = (1 ‐ x) cos x ‐ sin x = 0 has at least one root between a = 0 and b = 1 since f(a)f(b) < 0. The bisection method of finding the root proceeds as follows: a. It finds the midpoint r = (a + b)/2. b. If f(r) = 0, then r is the root. If |b ‐ a| is very small less than ∈ then also we can take r as the root....
QUESTION 1 = = (a) Apart from x = 0 the equation f(x) 22 – 4 sin r 0 has another root in (1, 2.5). Perform three iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x(0) = 1.5 as the initial solution. Compare the error from the Newton's approximation with that incurred for the same...
this is numerical analysis
QUESTION 1 (a) Apart from 1 = 0 the equation f(1) = x2 - 4 sin r = 0 has another root in (1, 2.5). Perform three (10) iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x) = 1.5 as the initial (10) solution. Compare the error from the Newton's approximation...
Find the general solution of the given differential equation. x y - y = x2 sin(x) y(x) = (No Response) Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) (No Response) Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.) (No Response)
Explain why the differential equation v' (I) – sin(x)+(x) + sin(v(x)) = 0) with initial condition (0) = 1 has a unique solution for all times < > 0.
Consider the following function #x)-x2/5, a-1, n-3, 0.7 sxs 1.3 (a) Approximate fby a Taylor polynomial with degree n at the number a T3(x) (b) Use Taylor's Inequality to estimate the accuracy of the approximation x) Tn(x) when x lies in the given interval. (Round your answer to eight decimal places.)
Consider the following function #x)-x2/5, a-1, n-3, 0.7 sxs 1.3 (a) Approximate fby a Taylor polynomial with degree n at the number a T3(x) (b) Use Taylor's Inequality to...
Consider the following differential equation.
(x2 − 4)
dy
dx
+ 4y = (x + 2)2
Consider the following differential equation. dy (x2 - 4) dx + 4y = (x + 2)2 Find the coefficient function P(x) when the given differential equation is written in the standard form dy dx + P(x)y = f(x). 4 P(x) = (x2 – 4) Find the integrating factor for the differential equation. SP(x) dx 1 Find the general solution of the given differential equation....
Consider the function: f (x) = b - sin(x), where bis an arbitrary number. Are roots always possible for any value of b? Yes No Consider the function: f (x) = a - tan(x), where a is an arbitrary number. Are roots always possible? True False
explain why newtons method doesnt work for finding the root of the
equation
x^3-3x+9=0
if the initial approximation is chosen to be x1=1
f(x)=x^3-3x+9 -> f'(x)= . if x1=1 then f'(x1)= and the
tangent line ued for approximating x2 is . attempting to find x^2
results in trying to by zero
1. [-/100 Points) DETAILS SCALCETS 4.8.031. MY NOTES Explain why Newton's method doesn't work for finding the root of the equation if the initial approximation is chosen to be...
Hi, need help with some Matlab problems. How would this be
entered?
1 (a) Let f(x) sin(x)-cos(x)-1. Calculate f(1) and f(2) and then explain why there is an [1.2] such that f(a)--0. You should give your values off to four significant decimal digits. (b) With a andb 2, the first two iterations of the bisection method for the function given in part (a) are shown in the following table. Do two more iterations to find the missing values in the...
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