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3 (i) Sketch y= 2* and y=x+2 on the same axes. (ii) Use your sketch to...
Problem #2/3 points total] 1. Graph 1lx2 -(22/2)x+Sy2 33 In your assignment submission, make sure that the scaling of both axes is the same (1 unit on the x-axis is the same length as 1 unit on t...
Problem #2/3 points total] 1. Graph 1lx2 -(22/2)x+Sy2 33 In your assignment submission, make sure that the scaling of both axes is the same (1 unit on the x-axis is the same length as 1 unit on the y axis) Insert the graph into your assignment submission. If necessary, scale the graph so that the scaling of both axes is the same Type or write, where you replace the italicized portion by your answer: The shape of the graph of...
[20 Marks] Question 2 a) Given f(x)= x - 7x2 +14x-6 i) Show that there is...
[20 Marks] Question 2 a) Given f(x)= x - 7x2 +14x-6 i) Show that there is a root a in interval [0,1] (1 mark) ii) Find the minimum number of iterations needed by the bisection method to approximate the root, a of f(x) = 0 on [0,1] with accuracy of 2 decimal points. (3 marks) iii) Find the root (a) of f(x)= x - 7x² +14x6 on [0,1] using the bisection method with accuracy of 2 decimal points. (6 marks)...
Question 3 Consider the ordinary differential equation (ODE) 2xy" + (1 + x)y' + 3y =...
Question 3 Consider the ordinary differential equation (ODE) 2xy" + (1 + x)y' + 3y = 0, in the neighbourhood of the origin. a) Show that x = 0 is a regular singular point of the ODE. (10) b) By seeking an appropriate solution to the ODE, show that G=- (10) i) the roots to the indicial equation of the ODE are 0 and 1/2. [10] ii) the recurrence formula used to determine the power series coefficients, ens when one...
The slope field for the equation y'=-x+y is shown above On a print out of this slope field, sketch the solutions that...
The slope field for the equation
y'=-x+y is shown above
On a print out of this slope field, sketch the solutions that
pass through the points
(i) (0,0);
(ii) (-3,1); and
(iii) (-1,0).
From your sketch, what is the equation of the solution to the
differential equation that passes through (-1,0)? (Verify that your
solution is correct by substituting it into the differential
equation.)
Q.2 and On Cartesian axes X - Y, sketch an accurate diagram of the quadratic functions...
Q.2 and On Cartesian axes X - Y, sketch an accurate diagram of the quadratic functions y. (x) = 3x - 2x yz (x) = x2, that is, (a) Find the points where yı (x) and yz (x) cut the X and Y axes and where y. (x) and y2 (x) intersect. (b) Find the area of the region enclosed by yı (x) and yz (x) [5x2 marks]
C2.3 Let X and Y be random variables with finite variance, so that EX2o0 (i) Show...
C2.3 Let X and Y be random variables with finite variance, so that EX2o0 (i) Show that E(X) - (EX) E(X - EX)2, and hence that the variance of (ii) By considering (|XI Y)2, or otherwise, show that XY has finite expecta- (iii) Let q(t) = E(X + tY)2. Show that q(t)2 0, and by considering the roots of and EY2 < oo. X is always non-negative. tion the equation q(t) 0, deduce that
1 2 NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the...
1
2
NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program,...
question 3 please The first 5 questions refer to finding solutions to the equation exp(w) =...
question 3 please
The first 5 questions refer to finding solutions to the equation exp(w) = 3.8 ln(1+x). You will need to write it in the form f(x)-0, and use various root finding methods. 1. (10 pts) Plot the curves y- exp(Vx), and y 3.8 ln(1+x) on the same graph in the range 0 x 6. Read off intervals in which there are roots of the equation exp(k)- 3.8 In(1+x) Now find the roots to 6 decimal places using the...
Sketch the signals with the figure given below. i. x(t+1)y(t-2) ii. x(4-t)y(2t) X(t) 1 2 3...
Sketch the signals with the figure given below.
i. x(t+1)y(t-2)
ii. x(4-t)y(2t)
X(t) 1 2 3 t -1 y(t) -2 -1 1 2 -1
Question 1. Consider these real-valued functions of two variables f(x, y) (a) (i) What is the max...
Question 1. Consider these real-valued functions of two variables f(x, y) (a) (i) What is the maximal domain, D, for the functions f and g? Write D in set notation (ii) What is the range of f and g? Is either function onto? (iii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: 20-0, 20-2, 20-4 (Note: Use set notation, and draw a single contour diagram.) (v) Without finding Vg, on your...
Problem #2/3 points total] 1. Graph 1lx2 -(22/2)x+Sy2 33 In your assignment submission, make sure that the scaling of both axes is the same (1 unit on the x-axis is the same length as 1 unit on the y axis) Insert the graph into your assignment submission. If necessary, scale the graph so that the scaling of both axes is the same Type or write, where you replace the italicized portion by your answer: The shape of the graph of...
[20 Marks] Question 2 a) Given f(x)= x - 7x2 +14x-6 i) Show that there is a root a in interval [0,1] (1 mark) ii) Find the minimum number of iterations needed by the bisection method to approximate the root, a of f(x) = 0 on [0,1] with accuracy of 2 decimal points. (3 marks) iii) Find the root (a) of f(x)= x - 7x² +14x6 on [0,1] using the bisection method with accuracy of 2 decimal points. (6 marks)...
Question 3 Consider the ordinary differential equation (ODE) 2xy" + (1 + x)y' + 3y = 0, in the neighbourhood of the origin. a) Show that x = 0 is a regular singular point of the ODE. (10) b) By seeking an appropriate solution to the ODE, show that G=- (10) i) the roots to the indicial equation of the ODE are 0 and 1/2. [10] ii) the recurrence formula used to determine the power series coefficients, ens when one...
The slope field for the equation
y'=-x+y is shown above
On a print out of this slope field, sketch the solutions that
pass through the points
(i) (0,0);
(ii) (-3,1); and
(iii) (-1,0).
From your sketch, what is the equation of the solution to the
differential equation that passes through (-1,0)? (Verify that your
solution is correct by substituting it into the differential
equation.)
Q.2 and On Cartesian axes X - Y, sketch an accurate diagram of the quadratic functions y. (x) = 3x - 2x yz (x) = x2, that is, (a) Find the points where yı (x) and yz (x) cut the X and Y axes and where y. (x) and y2 (x) intersect. (b) Find the area of the region enclosed by yı (x) and yz (x) [5x2 marks]
C2.3 Let X and Y be random variables with finite variance, so that EX2o0 (i) Show that E(X) - (EX) E(X - EX)2, and hence that the variance of (ii) By considering (|XI Y)2, or otherwise, show that XY has finite expecta- (iii) Let q(t) = E(X + tY)2. Show that q(t)2 0, and by considering the roots of and EY2 < oo. X is always non-negative. tion the equation q(t) 0, deduce that
1
2
NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program,...
question 3 please
The first 5 questions refer to finding solutions to the equation exp(w) = 3.8 ln(1+x). You will need to write it in the form f(x)-0, and use various root finding methods. 1. (10 pts) Plot the curves y- exp(Vx), and y 3.8 ln(1+x) on the same graph in the range 0 x 6. Read off intervals in which there are roots of the equation exp(k)- 3.8 In(1+x) Now find the roots to 6 decimal places using the...
Sketch the signals with the figure given below.
i. x(t+1)y(t-2)
ii. x(4-t)y(2t)
X(t) 1 2 3 t -1 y(t) -2 -1 1 2 -1
Question 1. Consider these real-valued functions of two variables f(x, y) (a) (i) What is the maximal domain, D, for the functions f and g? Write D in set notation (ii) What is the range of f and g? Is either function onto? (iii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: 20-0, 20-2, 20-4 (Note: Use set notation, and draw a single contour diagram.) (v) Without finding Vg, on your...
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