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pls do 25 and 27 function f(2) In Exercises 25-30 determine whether the expression can be...
Question 4(25 marks) Find the critical points of following function, then determine whether they are relative maximum, relative minimum or saddle points i. f(x,y) 3x2-2xyy2- 8y [Smarks] [5marks] [5marks] iii. f(x,y)--2x + 4y-x2-4y2 + 9 b) Find the divergence and curl of the following vector fields i. F(x, y, z) = x2 yi + 2y3zj + 3zk [5marks] ii. F(x, y,z) x sin y i+4xyz j - cos 3z k [5marks]
26. This exercise and Exercises 27 and 28 give Dirichlet's beautiful proof that 2 is a biquadratic residue modulo p iff p can be written in the form A 64B', where A, Be Z. Suppose that p1 (4). Thenp b by Exercise 24. Take a to be odd. Prove the following statements (a) (a/p)1 b) (a b)lp) a (c) (a b) 2ab (p. (d) (a b(2ab)4(p). [Hint: 2p (a + b)* + (a bJ p-1V2 P14 26. This exercise and...
Question 25, 27, 39 Question 25, 27, 39 For Exercises 25-32, use the following graph of F to find each limit. When necessary, state that the limit does not exist. YA 6 F 4 2 1 $-4-3-2-1 1 2 3 4 5 6 -3 25. lim F(x) 27. lim F(x) 29. lim F(x) 31. lim + F(x) x-2 X-5 26. lim F(x) X2 28. lim F(x) 30. lim F(x) X-6 32. lim_ F(x) --2- X4 For Exercises 33-40, use the...
Question 5 (25 points) : Use Lagrange multipliers to find all the critical points of the function f (x, y, z)-22on the surface 2 -4y2 722. You do not need to determine whether they are maxima, minima or saddle points. Question 5 (25 points) : Use Lagrange multipliers to find all the critical points of the function f (x, y, z)-22on the surface 2 -4y2 722. You do not need to determine whether they are maxima, minima or saddle points.
In Exercises 25-28, a net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v and the net is described by the given equations. 26. v = (x _ y, z + y 4, z~ ), net given by y = I-x2-z2, y 0, oriented in the positive y-direction In Exercises 25-28, a net is dipped in a river. Determine the flow rate of...
#35,37 In Exercises 21 through 38, differentiate the given function and simplify your answer 21. f(x) (2x 3)14 22. fx) 23. f(x) = (2x + 1)4 24. f(x) = V 5x6-12 25. fx)-(a 4r3 78 26. ft) (3r 729)5 27, f(t) = V5 3x 28. f(x)=- (6x2 +5x+ 1)2 5rt_ V4x2 30. 4x +1 31. f(x)=: (1-x2)4 2 3(5x4 1)2 32. f(x) = (1-x2)4 (135) f(x) = (x + 2)3(2x-1)5 36. f(x) 2(3x 1)(5x 3)2 (1 -x 1 - 5x2...
9,17,33 and ill like cos 22 14. 2+1 In Exercises 1-26 find the Taylor series for the function about the given point. In each case determine values of z for which the series converges to the function. 3 1. + about zo = 0 2. 1+2 about = 1 3. (1 - 2)2 about 20 = 0 4. e* about 20 = 1+i 5. sin z about 20 = i 6. cos z about zo = 2 - 7. sinh...
pls use the geogebra application to answer question 2 for me QUESTION 2 Verify whether f(x) is a probability density function (pdf) by going through the following steps. a. Enter the entries in the table into the spreadsheet view in GeoGebra b. Plot all pairs of points (x,f(x)) and fit an appropriate curve or polynomial to the points. c. Show, by shading, the region corresponding to the area under f(x) for the range of x values 0 SXS 4. d....
26 to 33 please! :) REVIEW EXERCISES: CHAPTER 2 149 2 Solve each formula for the given letter. 12.3] r 26. C rd, for d Bh, for B 27. V = 28. 5x 2y 10, for y 29· tx = ax + b, for x 30. Find decimal notation for 1.2%. [2.4] 31. Find percent notation for 2 12.4] 32. What percent of 60 is 42? 12.4] 33.49 is 35% of what number? [2.4] Determine whether each number is a...
2. For each function, find all critical points and use the Hessian to determine whether they are local maxima, minima, or saddle points. (a) f(x,y,z) = x — 2 sin x – 3yz (b) g(x, y, z) = cosh x + 4yz – 2y2 – 24 (c) u(x, y, z) = (x – z)4 – x2 + y2 + 6x2 – 22