![1. Consider the function y f(x) defined by Supposing that you are given x, write an R expression for y using if state- ments Add your expression for y to the following program, then run it to plot the function f. # input x,values <-seq(-2, 2, by 0.1) # for each x calculate y n <- length(x.values) y.values <- rep(0, n) for (i in 1 :n) x <- x. values[i] # your expression for y goes here y.values ij <- y # output plot(x.values, y.values, type1) Your plot should look like Figure 3.2. Do you think f has a derivative at 1? What about at 0? We remark that it is possible to vectorise the program above, using the ifelse function.](http://img.homeworklib.com/questions/dc633e70-739b-11ea-881e-4d3b27e94b92.png?x-oss-process=image/resize,w_560)
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1. Consider the function y f(x) defined by Supposing that you are given x, write an...
1. Consider the function y f(x) defined by Supposing that you are given x, write an...
1. Consider the function y f(x) defined by Supposing that you are given x, write an R expression for y using if state- ments Add your expression for y to the following program, then run it to plot the function f. # input x,values <-seq(-2, 2, by 0.1) # for each x calculate y n <- length(x.values) y.values <- rep(0, n) for (i in 1 :n) x <- x. values[i] # your expression for y goes here y.values ij <-...
1. Consider the function y - f(x) defined by Supposing that you are given x, write...
1. Consider the function y - f(x) defined by Supposing that you are given x, write an R expression for y using if state- ments. Add your , then run it to plot the function jf # input x.values <- seq(-2, 2, by - 0.1) expression for y to the following program # for each x calculate y n <- length(x.values) y.values <- rep(0, n) for (i in 1:n) t x <- x.values [i] # your expression for y goes...
3. (a) Write a MatLab program that calculates for the function F(x, y) = ln(x + Va,2-y2) The prog...
3. (a) Write a MatLab program that calculates for the function F(x, y) = ln(x + Va,2-y2) The program should use pretty) to display both the original function and the differentiated result, and also use fprintf() to print a label such as "F(x,y) -" and "dF/dxdy - " in front of both the function and the derivative. Then have your program also print out the derivative again after it uses simplify() on the result (b) Find the Taylor expansion of...
1. (25 pts) Let f(x) be a continuous function and suppose we are already given the Matlab function "f.", with header "function y fx)", that returns values of f(x) Given the following...
1. (25 pts) Let f(x) be a continuous function and suppose we are already given the Matlab function "f.", with header "function y fx)", that returns values of f(x) Given the following header for a Matlab function: function [pN] falseposition(c,d,N) complete the function so that it outputs the approximation pN, of the method of false position, using initial guesses po c,pd. You may assume c<d and f(x) has different signs at c and d, however, make sure your program uses...
Consider the function f : {0,1} » N → NU{0} defined as f(x,y) = (-1)22 y....
Consider the function f : {0,1} » N → NU{0} defined as f(x,y) = (-1)22 y. Is f injective? Surjective? Explain your answer.
-100x 1. Given the function f(x)=- (1-0.5x) (a) Find the y-intercept point (if there is any):...
-100x 1. Given the function f(x)=- (1-0.5x) (a) Find the y-intercept point (if there is any): (b) Find the x-intercept point(s) (if there is any): (c) Find f'(x): (d) Find critical number(s) of f(x) (Type 1 and Type 2, if there are any): (e) Find the critical point(s) (if there are any): (f) Find the open x-intervals where f(x) increases and decreases: (g) Find the behavior of the function for very large positive x-values (find limit as x goes to...
(1 point) The density function f (xl) = he-hx, is defined for <x< , with parameter...
(1 point) The density function f (xl) = he-hx, is defined for <x< , with parameter 1 > 0. The likelihood function for the parameter 2 given n independent observations x = (X1, X2,...,xn) is L(xl2) = "e-1E1. Suppose three independent observations X1, X2 and X3 are taken and found to be 0.5447, 1.0291, 1.722. Parta) Evaluate, to two decimal places, the likelihood function for the data given at the point i = 1.26. Below is a plot of the...
Consider the function f(x) = x ln(3x+1) (a) Find the derivative (b) Write the linearization of...
Consider the function f(x) = x ln(3x+1) (a) Find the derivative (b) Write the linearization of f at x = 2 (c) Use your linearization to estimate f(2.5) (d) Draw a sketch of the function in the space below, using a solid line for f(x). On the same coordinate plane, draw a sketch of the linearization using a dotted line. Please use values 0<x<5(or equal to) on the x-axis (e) Is your estimate from part c an overestimate or underestimate?
(1 point) Consider the function f (x, y) = 3x2 + 4y2. f at the point (-4,1) in the direction given by Find the the dire...
(1 point) Consider the function f (x, y) = 3x2 + 4y2. f at the point (-4,1) in the direction given by Find the the directional derivative of the angle 0 Find the vector which describes the direction in which f is increasing most rapidly at (-4, 1)
(1 point) Consider the function f (x, y) = 3x2 + 4y2. f at the point (-4,1) in the direction given by Find the the directional derivative of the angle 0 Find...
5. [12 Marks) Consider the level surface of the function f(x, y, z) defined by f(x,...
5. [12 Marks) Consider the level surface of the function f(x, y, z) defined by f(x, y, z) = x2 + y2 + x2 = 2a?, (1) where a is a fixed real positive constant, and the point u = (0,a,a) on the surface f(x, y, z) = 2a. a) Find the gradient of f(x, y, z) at the point u. b) Calculate the normal derivative of f(x, y, 2) at u. c) Find the equation of the tangent plane...
1. Consider the function y f(x) defined by Supposing that you are given x, write an R expression for y using if state- ments Add your expression for y to the following program, then run it to plot the function f. # input x,values <-seq(-2, 2, by 0.1) # for each x calculate y n <- length(x.values) y.values <- rep(0, n) for (i in 1 :n) x <- x. values[i] # your expression for y goes here y.values ij <-...
1. Consider the function y - f(x) defined by Supposing that you are given x, write an R expression for y using if state- ments. Add your , then run it to plot the function jf # input x.values <- seq(-2, 2, by - 0.1) expression for y to the following program # for each x calculate y n <- length(x.values) y.values <- rep(0, n) for (i in 1:n) t x <- x.values [i] # your expression for y goes...
3. (a) Write a MatLab program that calculates for the function F(x, y) = ln(x + Va,2-y2) The program should use pretty) to display both the original function and the differentiated result, and also use fprintf() to print a label such as "F(x,y) -" and "dF/dxdy - " in front of both the function and the derivative. Then have your program also print out the derivative again after it uses simplify() on the result (b) Find the Taylor expansion of...
1. (25 pts) Let f(x) be a continuous function and suppose we are already given the Matlab function "f.", with header "function y fx)", that returns values of f(x) Given the following header for a Matlab function: function [pN] falseposition(c,d,N) complete the function so that it outputs the approximation pN, of the method of false position, using initial guesses po c,pd. You may assume c<d and f(x) has different signs at c and d, however, make sure your program uses...
Consider the function f : {0,1} » N → NU{0} defined as f(x,y) = (-1)22 y. Is f injective? Surjective? Explain your answer.
-100x 1. Given the function f(x)=- (1-0.5x) (a) Find the y-intercept point (if there is any): (b) Find the x-intercept point(s) (if there is any): (c) Find f'(x): (d) Find critical number(s) of f(x) (Type 1 and Type 2, if there are any): (e) Find the critical point(s) (if there are any): (f) Find the open x-intervals where f(x) increases and decreases: (g) Find the behavior of the function for very large positive x-values (find limit as x goes to...
(1 point) The density function f (xl) = he-hx, is defined for <x< , with parameter 1 > 0. The likelihood function for the parameter 2 given n independent observations x = (X1, X2,...,xn) is L(xl2) = "e-1E1. Suppose three independent observations X1, X2 and X3 are taken and found to be 0.5447, 1.0291, 1.722. Parta) Evaluate, to two decimal places, the likelihood function for the data given at the point i = 1.26. Below is a plot of the...
(1 point) Consider the function f (x, y) = 3x2 + 4y2. f at the point (-4,1) in the direction given by Find the the directional derivative of the angle 0 Find the vector which describes the direction in which f is increasing most rapidly at (-4, 1)
(1 point) Consider the function f (x, y) = 3x2 + 4y2. f at the point (-4,1) in the direction given by Find the the directional derivative of the angle 0 Find...
5. [12 Marks) Consider the level surface of the function f(x, y, z) defined by f(x, y, z) = x2 + y2 + x2 = 2a?, (1) where a is a fixed real positive constant, and the point u = (0,a,a) on the surface f(x, y, z) = 2a. a) Find the gradient of f(x, y, z) at the point u. b) Calculate the normal derivative of f(x, y, 2) at u. c) Find the equation of the tangent plane...
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