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Numerical Methods C3 HELP ??

11. Copy this sketch of the curve with equation y=(e^-x)-1. On the same axes sketch the graph of y=1/2(x-1), for x>(or equal to)1, and y=-1/2(x-1), for x <1.
Show the coordinates of the piont where the graph meets the axes

(done this)

The x-coordinate of the point of intersection of the graphs is alpha.

b) Show that x=alpha is a root of the equation x + 2e^(-x) - 3=0.

I have done this but it would help if you could do it too just so I could see if I am right.

c) Show that -1<alpha<0.

Done this.


The iterative formula x n+1 = -ln(1/2(3-xn)) is used to solve the equation x + 2e^-x - 3 = 0.

d) Starting with x0 = -1, find the value of x1 and x2.

Done this.

x1 = -0.6931
x2 = -0.6133

e) Show that to 2 decimal places, a = -0.58

This is the part I don't understand.

In general, I am confused about these types of questions so it would really help if you could explain them.

Thank you.
Reply 1
Avatar for TeeEm
TeeEm
19
Original post by alishahussain832
11. Copy this sketch of the curve with equation y=(e^-x)-1. On the same axes sketch the graph of y=1/2(x-1), for x>(or equal to)1, and y=-1/2(x-1), for x <1.
Show the coordinates of the piont where the graph meets the axes

(done this)

The x-coordinate of the point of intersection of the graphs is alpha.

b) Show that x=alpha is a root of the equation x + 2e^(-x) - 3=0.

I have done this but it would help if you could do it too just so I could see if I am right.

c) Show that -1<alpha<0.

Done this.


The iterative formula x n+1 = -ln(1/2(3-xn)) is used to solve the equation x + 2e^-x - 3 = 0.

d) Starting with x0 = -1, find the value of x1 and x2.

Done this.

x1 = -0.6931
x2 = -0.6133

e) Show that to 2 decimal places, a = -0.58

This is the part I don't understand.

In general, I am confused about these types of questions so it would really help if you could explain them.

Thank you.


dear alishahussain832

I think the student room is lacking volunteers and I am unable to help you.
This is probably because it is Sturday night.
However I feel your question is too open, in other words if you do not understand most of this you will better off to ask your teacher or go to a self teaching site like exam solutions.
Original post by alishahussain832
11. Copy this sketch of the curve with equation y=(e^-x)-1. On the same axes sketch the graph of y=1/2(x-1), for x>(or equal to)1, and y=-1/2(x-1), for x <1.
Show the coordinates of the piont where the graph meets the axes

(done this)

The x-coordinate of the point of intersection of the graphs is alpha.

b) Show that x=alpha is a root of the equation x + 2e^(-x) - 3=0.

I have done this but it would help if you could do it too just so I could see if I am right.

c) Show that -1<alpha<0.

Done this.


The iterative formula x n+1 = -ln(1/2(3-xn)) is used to solve the equation x + 2e^-x - 3 = 0.

d) Starting with x0 = -1, find the value of x1 and x2.

Done this.

x1 = -0.6931
x2 = -0.6133

e) Show that to 2 decimal places, a = -0.58

This is the part I don't understand.

In general, I am confused about these types of questions so it would really help if you could explain them.

Thank you.


Continue the iteration on your calculator writing down subsequent values of x obtained until you reach the required value (-0.58)
Original post by alishahussain832
e) Show that to 2 decimal places, a = -0.58


Hi

This is the same as showing that the solution is between -0.585 and -0.575

Do you know how to show that a solution lies within a given interval?
Reply 4
Avatar for Gome44
Gome44
10
Original post by alishahussain832
11. Copy this sketch of the curve with equation y=(e^-x)-1. On the same axes sketch the graph of y=1/2(x-1), for x>(or equal to)1, and y=-1/2(x-1), for x <1.
Show the coordinates of the piont where the graph meets the axes

(done this)

The x-coordinate of the point of intersection of the graphs is alpha.

b) Show that x=alpha is a root of the equation x + 2e^(-x) - 3=0.

I have done this but it would help if you could do it too just so I could see if I am right.

c) Show that -1<alpha<0.

Done this.


The iterative formula x n+1 = -ln(1/2(3-xn)) is used to solve the equation x + 2e^-x - 3 = 0.

d) Starting with x0 = -1, find the value of x1 and x2.

Done this.

x1 = -0.6931
x2 = -0.6133

e) Show that to 2 decimal places, a = -0.58

This is the part I don't understand.

In general, I am confused about these types of questions so it would really help if you could explain them.

Thank you.


Let f(x)=x+2e^-x -3

You are looking to show that a=-0.58 to two dp, so try f(-0.585) and f(-0.575). Both of these are the lower and upper bounds of -0.58 to 2 dp. This means both these numbers and any in between would round -0.58 to 2 dp
(edited 9 years ago)
Thank you everyone. I figured it out in the end. I did exactly what you all suggested. So thank you very much for taking the time to respond.

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