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Let f(x,y) = 4 + x3 - 2y2. Find the gradient of f(x,y) at (1,1,3). Find the dire

Let f(x,y) = 4 + x3 - 2y2. Find the gradient of f(x,y) at (1,1,3). Find the direction in the xy plane that gives the steepest descent on the graph of f(x,y) away from the point (1…

Let f(x,y)=1+x^2cos(5y). Find all critical points and classify them as local max

Let f(x,y)=1+x^2cos(5y). Find all critical points and classify them as local maxima, local minima, saddle points, or none of these. critical points: __________ (give your points a…

Let f(x,y)=ln(x^2+y^2+1) +e^(2xy): find the gradient of f at the point (0,-2) b)

Let f(x,y)=ln(x^2+y^2+1) +e^(2xy): find the gradient of f at the point (0,-2) b)Find the directional derivative of f at the point (0,-2) c)Find the maximum value of the directiona…

Let f(x,y)=x^3y and c(t)=(2t^2,t^3) (b) Use the chain rule for paths to evaluate

Let f(x,y)=x^3y and c(t)=(2t^2,t^3) (b) Use the chain rule for paths to evaluate d/df f(c(t)) at t=-1 Let f(x,y) = x^3y and c(t) = (2t^2,t^3) (a) Calculate: Nabla f.c(t)= 12x^2yt+…

Let f(z) = z, g(z) = (z-4)\", h(z) \"\" (z-4 ). 7, and p(z)-3(z-4)2 + 7 a. Deter

Let f(z) = z, g(z) = (z-4)", h(z) "" (z-4 ). 7, and p(z)-3(z-4)2 + 7 a. Determine the root(s) of the functions defined above. Enter your answer as a number of string of numbers. S…

Let f(z) be analytic in some domain. Show that f(z) is necessarily a constant if

Let f(z) be analytic in some domain. Show that f(z) is necessarily a constant if either the conjugate of f(z) is analytic or f(z) assumes only pure imaginary values in the domain.

Let f(z) be analytic in some domain. Show that f(z) is necessarily a constant if

Let f(z) be analytic in some domain. Show that f(z) is necessarily a constant if either the conjugate of f(z) is analytic or f(z) assumes only pure imaginary values in the domain.

Let f: A to B be function between two sets A and B Show that the following are t

Let f: A to B be function between two sets A and B Show that the following are true: 1- f in injective IF AND ONLY IF every b that belongs to B, the set inverse of functionof (b) …

Let f: R -> S be a homomorphism of rings and let K = {r element of R | f(r) = 0s

Let f: R -> S be a homomorphism of rings and let K = {r element of R | f(r) = 0s}. Prove that K is a subring of R. Please show all steps and describe how you proceeded, clearly…

Let f: R^2 - { (0, 0)) rightarrow R be defined by f(z, y) = (2x + y)^2/x^2 + y^2

Let f: R^2 - { (0, 0)) rightarrow R be defined by f(z, y) = (2x + y)^2/x^2 + y^2. a) Can f be defined at (0, 0) so that f is continuous there? That is, does there exist a real num…

Let f: R^2 rightarrow R be a \"smooth\" function and X R^2. If X is a compact su

Let f: R^2 rightarrow R be a "smooth" function and X R^2. If X is a compact subset of R^2 and the gradient of f is never equal to the zero vector on X, what can yo say about the p…

Let f: R^2 rightarrow R be a \"smooth\" function and X R^2. If X is a compact su

Let f: R^2 rightarrow R be a "smooth" function and X R^2. If X is a compact subset of R^2 and the gradient of f is never equal to the zero vector on X, what can you say about the …

Let f: R^3 rightarrow R^3 with f(x, y, z) = (x - 2y + z, -2x - 2y + 2z, -3x - 3y

Let f: R^3 rightarrow R^3 with f(x, y, z) = (x - 2y + z, -2x - 2y + 2z, -3x - 3y + 3z) Does (1, 2, 3) belong to ker (f)? Does (1, 2, 3) belong to im(f)? Let f be as in question 4.…

Let f: S right arrow be a function and let A be a subset of S. Prove that A cele

Let f: S right arrow be a function and let A be a subset of S. Prove that A celementof f^-1(f(A)). Let f: S rightarrow T be a function. Let A and B be subsets of S and C and be su…

Let f: V --> W be an isomorphism (i.t. a rule that is one-to-one, onto and prese

Let f: V --> W be an isomorphism (i.t. a rule that is one-to-one, onto and preserves additon and salign in the sense that f(v+w) = f(v) + f(w) and f(cv) = cf(v)). Suppose that …

Let f: X rightarrow R {infinity} be a function, for some metric space X. We defi

Let f: X rightarrow R {infinity} be a function, for some metric space X. We define "regularizations" f_(-), f_(s) off by f_(-)(x): = sup{g(x): g lessthanorequalto f, g: X rightarr…

Let f: X rightarrow Y be a map and A_1, A_2 Subset X. Prove that f(A_1Intersecti

Let f: X rightarrow Y be a map and A_1, A_2 Subset X. Prove that f(A_1Intersection A_2) Subset f(A_1)Intersection f(A_2). Show by example that the equality might fail. Let f: X ri…

Let f: [0, 1] leftarrow Q be a continuous function such that f(0) = 0. Construct

Let f: [0, 1] leftarrow Q be a continuous function such that f(0) = 0. Construct an argument to determine the value of f(squareroot2/2). Let f be a continuous function from R into…

Let f: [0,1] to R(eal numbers) be a function that maps closed and bounded interv

Let f: [0,1] to R(eal numbers) be a function that maps closed and bounded intervals onto closed and bounded intervals, hence if 0 <(or equal to) a < b <(or equal to) 1, t…

Let f: [a, b] rightarrow R be a bounded function. Prove that the following condi

Let f: [a, b] rightarrow R be a bounded function. Prove that the following conditions on f are equivalent: f is integrable on [a,b]; there exists a sequence (Q_n) of partitions of…

Let f:A->B and g:C->D be functions. Disprove if g o f is 1-1 then g is 1-1. Solu

Let f:A->B and g:C->D be functions. Disprove if g o f is 1-1 then g is 1-1.

Let f:U-->V and g:V--->W be two linear maps, and let gf:U--->W be the compositio

Let f:U-->V and g:V--->W be two linear maps, and let gf:U--->W be the composition of f and g. (a) If gf is injective then f is injective, but g may not be injective. Give…

Let f:X->Y and g:Y->Z, prove that gof is onto and one-to-one if both g and f are

Let f:X->Y and g:Y->Z, prove that gof is onto and one-to-one if both g and f are.

Let f:X->Y and g:Y->Z, show that g is surjective, if gof is surjective. Solution

Let f:X->Y and g:Y->Z, show that g is surjective, if gof is surjective.

Let f=(x1,x2,...,xr) be in Sn. Show that o(f) = r Solution consider f^r. That is

Let f=(x1,x2,...,xr) be in Sn. Show that o(f) = r

Let f_n(x) = 1+2cos^2nx/Squarerootn. Prove carefully that (f_n) converges unifor

Let f_n(x) = 1+2cos^2nx/Squarerootn. Prove carefully that (f_n) converges uniformly to 0 on R. 24.2 For x [0, infinity), let f_n(x) = x/n. (a) Find f(x) = lim f_n(x). (b) Determin…

Let fbe the function defined as follows (a) Find the differential of f (b) Use y

Let fbe the function defined as follows (a) Find the differential of f (b) Use your result from part (a) to find the approximate change in y if x changes from 2 to 1.97. (Round yo…

Let fc : M represent the channel coding map, where M is the set of message words

Let fc : M represent the channel coding map, where M is the set of message words and C is the set of code words. For a linear block code, fe, one can obtain a matrix representatio…

Let fg(x, y) = ln(x +(x^2 + y^2 )^(0.5)). (a) Find the domain of g. (b) Calculat

Let fg(x, y) = ln(x +(x^2 + y^2 )^(0.5)). (a) Find the domain of g. (b) Calculate the derivative Du f in the direction of i + j. (c) Find the linear approximation of f around the …

Let food be thy medicine and medicine be thy food.-- Hippocrates (460 - 370 BCE)

Let food be thy medicine and medicine be thy food.-- Hippocrates (460 - 370 BCE), the famous Greek physician Good Farms Company is a publicly held corporation. It sells grows and …

Let function f: Z nonneg x Z nonneg to Z nonneg f(0,y)=1 for all y >=0 f(1,0)=2

Let function f: Z nonneg x Z nonneg to Z nonneg f(0,y)=1 for all y >=0 f(1,0)=2 f(x,0)=x+2, x>=2 f(x+1, y+1)=f(f(x,y+1),y) 1. Find a formula (closed form) in terms of x to d…

Let g ( x ) = , where f is the function whose graph is shown. (a) Evaluate g (0)

Let g(x) = , where f is the function whose graph is shown. (a) Evaluate g(0), g(3), g(6), g(9) and g(18). (b) On what interval is g increasing? (  ,  ) (c) Where does g have a max…

Let g (x) = 3x/4 + 64/x^3. a. find the positive fixed point of g. b. find an int

Let g (x) = 3x/4 + 64/x^3. a. find the positive fixed point of g. b. find an interval [a, 6], containing the fixed point found in part (a), in which g(x) elementof [a, 6] whenever…

Let g(x) = f(t) dt, where f is the function whose graph is shown. (a) Evaluate g

Let g(x) = f(t) dt, where f is the function whose graph is shown. (a) Evaluate g(x) for x=0,4,8,12,16,20,and 24 (b) Estimate g(28). (use the midpoint to get the most preside estim…

Let g(x) = write a program (using Matlab/Octave or C/C++) that implements fixed

Let g(x) = write a program (using Matlab/Octave or C/C++) that implements fixed point iteration as discussed in class (i.e., do not use any built-in fixed point iteration function…

Let g(x)= x + 7/x^2 + 5x -14. Determine all values of x at which g is discontinu

Let g(x)= x + 7/x^2 + 5x -14. Determine all values of x at which g is discontinuous, and for each of these values of x, define g in such a manner as to remove the discontinuity, i…

Let g1 be the annualized growth rate from period 0 to period 1 and let g2 be the

Let g1 be the annualized growth rate from period 0 to period 1 and let g2 be the annualized growth rate from period 1 to period 2. Let g_average= (g1 + g2)/2 be the average of the…

Let give the area in square miles of a town in year , and the area in square kil

Let give the area in square miles of a town in year , and the area in square kilometers. Find a formula for by scaling the output of . Use the fact that 1 mile equals 1.609 kilome…

Let h :from G to G\' and g : from G to G\'\' be group homomorphisms, in which G,

Let h :from G to G' and g : from G to G'' be group homomorphisms, in which G, G' and G'' are groups. Denote the identity elements of G, G' and G'' by e, e' and e'' respectively. (…

Let h :from G to G\' and g : from G to G\'\' be group homomorphisms, in which G,

Let h :from G to G' and g : from G to G'' be group homomorphisms, in which G, G' and G'' are groups. Denote the identity elements of G, G' and G'' by e, e' and e'' respectively. (…

Let h = T/N be the length of one time-step in the binomial tree model. Set u = e

Let h = T/N be the length of one time-step in the binomial tree model. Set u = exp ( square root of h) and d = exp ( - square root of h), Fix T = 1, = 0.4, S(0) = K = 100 and inte…

Let h = h(t) be the function h(t) = 2 sigma^infinity_ n=0 (-1)^n u(t - n). Find

Let h = h(t) be the function h(t) = 2 sigma^infinity_ n=0 (-1)^n u(t - n). Find the Laplace transform of h. Determine the general solution of the ODE for y = y(t), y' + 2y = h. Id…

Let h be the height of release relative to ground level. Choose ground level as

Let h be the height of release relative to ground level. Choose ground level as the zero of gravitational potential energy. Let vi be the initial speed of the ball, and let vf be …

Let h be the height of release relative to ground level. Choose ground level as

Let h be the height of release relative to ground level. Choose ground level as the zero of gravitational potential energy. Let v_i, be the initial speed of the ball, and let v_f …

Let h be the height of release relative to ground level. Choose ground level as

Let h be the height of release relative to ground level. Choose ground level as the zero of gravitational potential energy. Let v_i, be the initial speed of the ball, and let v_f …

Let h be the homomorphism defined by h(a) = 01, h(b) = 10, h(c) = 0, and h(d) =

Let h be the homomorphism defined by h(a) = 01, h(b) = 10, h(c) = 0, and h(d) = 1. If we take any string w in (0+1)*, h-1(w) contains some number of strings, N(w). For example, h-…

Let i be a function from the set A to the set B. Let Sbe a subset of E. We defin

Let i be a function from the set A to the set B. Let Sbe a subset of E. We define the inverse image of S to be the subset of A whose lements are precisely all pre-images of all el…

Let ilselect(A, n, i) be an algorithm that selects the i-smallest from an array

Let ilselect(A, n, i) be an algorithm that selects the i-smallest from an array A with n integers. It works as follows: ilselect(A, n, i) {    r=partition(A, 1, n);    //test if A…

Let ilselect(A, n, i) be an algorithm that selects the i-smallest from an array

Let ilselect(A, n, i) be an algorithm that selects the i-smallest from an array A with n integers. It works as follows: ilselect(A, n, i) {    r=partition(A, 1, n);    //test if A…

Let ilselect(A, n, i) be an algorithm that selects the i-smallest from an array

Let ilselect(A, n, i) be an algorithm that selects the i-smallest from an array A with n integers. It works as follows: ilselect(A, n, i) {    r=partition(A, 1, n);    //test if A…