Homework Answers
Algebrically the this funxtion is a function of two variables of type z=(x,y) given by
The domain of the function is any plane 
of
.Algebra of function says the function can take all orderd pairs as
input except
So domain of f(x,y) is the set
The squareroot is always non-negative so we have range
Functions of two variables geometrically represent by means of
SURFACES. the graph of the function 
consists of ordered triples 
. The graph of a function of two variables
is called a surface.
Actually here each pair of independent variables 
and 
is
associated with the real number 
.as
shown below
The graph of f(x,y) tells us that as the x, y moves in the domain of definition the function winds up a surface passing through the z-axis evolving a 3D plane as shown below,(has imaginary part too)
Add Answer to:
specify the definition set of this function algebraically and
geometrically
f(x, y) = x+y X-у
5. Let f R2 ->R2 be the function given by f(x, y) (х + у, х...
5. Let f R2 ->R2 be the function given by f(x, y) (х + у, х — у). (i) Prove that f is linear as a function from R2 to R2. (ii) Calculatee the matrix of f. (iii) Prove that f is a one-to-one function whose range is R2. Deduce that f has an inverse function and calculate it. (iv) If C is the square in R2 given by C = [0,1] x [0, 1], find the set f(C), illustrating...
arbitrary continuous function f(x, y, z) in spherical coordinates over the solid shown Set up the...
arbitrary continuous function f(x, y, z) in spherical coordinates over the solid shown Set up the triple integral of an (Assume a 1 and b = 3.) f(x, у, z) dv = Ju/2 C фр Өр др
arbitrary continuous function f(x, y, z) in spherical coordinates over the solid shown Set up the triple integral of an (Assume a 1 and b = 3.) f(x, у, z) dv = Ju/2 C фр Өр др
Definition 5.48. Let f,g:X + Y be functions and assume that Y is a set in...
Definition 5.48. Let f,g:X + Y be functions and assume that Y is a set in which the following operations make sense. Then the following are also functions: 1. f + g defined by (f +g)(x) = f(x) + g(x) for all x E X 2. f - g defined by (f – g)(x) = f(x) – g(x) for all x € X 3. f.g defined by (fºg)(x) = f(x) · g(x) for all x E X f(x) = "147...
(5) Let Y,... Y2 be independent random variables from a distribution with distribution function P(У у-F(y),...
(5) Let Y,... Y2 be independent random variables from a distribution with distribution function P(У у-F(y), and density function f(s). Now let yl) be the minim um of all the observations. Show that the density function of Yu) is given by ow let Y(1 Yo ()n(1 - F(w)-f(w) Hint: First write out the CDF. P(W1) y), then using independence of the observations put it in terms of the distribution function F(), and then take the derivative to get the density.]
Given the function F(x,y) = y'+(x+y) : a) Make a truth table for F. [4 marks]...
Given the function F(x,y) = y'+(x+y) : a) Make a truth table for F. [4 marks] b) Express F as a sum of products. [3 marks] c) Simplify F, either algebraically or by an explanation based upon the truth table. [3 marks]
1. What is x(g(f(x)) = x)) (Hint: try to construct one such g) n-1 ing the definition of summatio...
1. What is x(g(f(x)) = x)) (Hint: try to construct one such g) n-1 ing the definition of summation symbol, we see that f(n)- f(n-1)+f(n-1) hence we can define f as f-{(my) є N N : (n-ОЛ у-1) v (n > 0A3y, E N(n-1, y') є f Лу = y, +y®)), and show that this is a function by induction.)
1. What is x(g(f(x)) = x)) (Hint: try to construct one such g) n-1 ing the definition of summation symbol,...
1. What is x(g(f(x)) = x)) (Hint: try to construct one such g) n-1 ing the definition of summatio...
1. What is x(g(f(x)) = x)) (Hint: try to construct one such g) n-1 ing the definition of summation symbol, we see that f(n)- f(n-1)+f(n-1) hence we can define f as f-{(my) є N N : (n-ОЛ у-1) v (n > 0A3y, E N(n-1, y') є f Лу = y, +y®)), and show that this is a function by induction.)
1. What is x(g(f(x)) = x)) (Hint: try to construct one such g) n-1 ing the definition of summation symbol,...
Answer the questions in the space provided below. 1. The definition of a function f: X...
Answer the questions in the space provided below. 1. The definition of a function f: X + Y is as a certain subset of the product X x Y. Let f: N + N be the function defined by the equation f(n) = n2. For each pair (x, y) listed below, determine whether or not (x,y) ef. a) (2,4) b) (5, 23) c) (1,1) d) (-3,9) 2. For each function defined below, state whether it is injective (one-to-one) and whether...
Use the graph of the function to solve the equation or inequality. у y = g(x)...
Use the graph of the function to solve the equation or inequality. у y = g(x) 5 (3, 4) X -5 5 y = f(x) (-1,-4) (a) f(x) = g(x) (Enter your answers as a comma-separated list.) X = (6) f(x) = g(x) (Enter your answer using interval notation.) (c) f(x) > g(x) (Enter your answer using interval notation.)
Question 1. 30% Given the function f(x, y) = e 1. Specify the domain and range...
Question 1. 30% Given the function f(x, y) = e 1. Specify the domain and range of f. 2. Describe the level curves off and graph the one that passes through the point (2,4). 3. Find the limit, if possible, when (x,y) approaches (0,0) of the function f(x,y). 4. Find the equation of the tangent plane and the normal line to surface defined by at the point (1,1,e). 5. We now let x = 12 and y = In 3t...
5. Let f R2 ->R2 be the function given by f(x, y) (х + у, х — у). (i) Prove that f is linear as a function from R2 to R2. (ii) Calculatee the matrix of f. (iii) Prove that f is a one-to-one function whose range is R2. Deduce that f has an inverse function and calculate it. (iv) If C is the square in R2 given by C = [0,1] x [0, 1], find the set f(C), illustrating...
arbitrary continuous function f(x, y, z) in spherical coordinates over the solid shown Set up the triple integral of an (Assume a 1 and b = 3.) f(x, у, z) dv = Ju/2 C фр Өр др
arbitrary continuous function f(x, y, z) in spherical coordinates over the solid shown Set up the triple integral of an (Assume a 1 and b = 3.) f(x, у, z) dv = Ju/2 C фр Өр др
Definition 5.48. Let f,g:X + Y be functions and assume that Y is a set in which the following operations make sense. Then the following are also functions: 1. f + g defined by (f +g)(x) = f(x) + g(x) for all x E X 2. f - g defined by (f – g)(x) = f(x) – g(x) for all x € X 3. f.g defined by (fºg)(x) = f(x) · g(x) for all x E X f(x) = "147...
(5) Let Y,... Y2 be independent random variables from a distribution with distribution function P(У у-F(y), and density function f(s). Now let yl) be the minim um of all the observations. Show that the density function of Yu) is given by ow let Y(1 Yo ()n(1 - F(w)-f(w) Hint: First write out the CDF. P(W1) y), then using independence of the observations put it in terms of the distribution function F(), and then take the derivative to get the density.]
1. What is x(g(f(x)) = x)) (Hint: try to construct one such g) n-1 ing the definition of summation symbol, we see that f(n)- f(n-1)+f(n-1) hence we can define f as f-{(my) є N N : (n-ОЛ у-1) v (n > 0A3y, E N(n-1, y') є f Лу = y, +y®)), and show that this is a function by induction.)
1. What is x(g(f(x)) = x)) (Hint: try to construct one such g) n-1 ing the definition of summation symbol,...
1. What is x(g(f(x)) = x)) (Hint: try to construct one such g) n-1 ing the definition of summation symbol, we see that f(n)- f(n-1)+f(n-1) hence we can define f as f-{(my) є N N : (n-ОЛ у-1) v (n > 0A3y, E N(n-1, y') є f Лу = y, +y®)), and show that this is a function by induction.)
1. What is x(g(f(x)) = x)) (Hint: try to construct one such g) n-1 ing the definition of summation symbol,...
Answer the questions in the space provided below. 1. The definition of a function f: X + Y is as a certain subset of the product X x Y. Let f: N + N be the function defined by the equation f(n) = n2. For each pair (x, y) listed below, determine whether or not (x,y) ef. a) (2,4) b) (5, 23) c) (1,1) d) (-3,9) 2. For each function defined below, state whether it is injective (one-to-one) and whether...
Use the graph of the function to solve the equation or inequality. у y = g(x) 5 (3, 4) X -5 5 y = f(x) (-1,-4) (a) f(x) = g(x) (Enter your answers as a comma-separated list.) X = (6) f(x) = g(x) (Enter your answer using interval notation.) (c) f(x) > g(x) (Enter your answer using interval notation.)
Question 1. 30% Given the function f(x, y) = e 1. Specify the domain and range of f. 2. Describe the level curves off and graph the one that passes through the point (2,4). 3. Find the limit, if possible, when (x,y) approaches (0,0) of the function f(x,y). 4. Find the equation of the tangent plane and the normal line to surface defined by at the point (1,1,e). 5. We now let x = 12 and y = In 3t...
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