II. Consider the function g defined by 1 g(x, y) = cos (Tx Vy) + log3(x – y) | 1. Determine dydx 2. In what direction does g have the maximum directional derivative at (x, y) = (4, 1)? What is the maximum directional derivative?

Q: C. Answer each. Find the number of different arrangements of the set of the seven letters…

A: Let us solve using permutations.

Q: Let W = {a + bx +x2 E P2: a, b ER} with the standard operations in P2. Which of the following…

A:

Q: 2. Determine whether the following subset S of R3 is a subspace or not. a) S = X2||x1x2x3 = X3 S.…

A: Let V be a vector space over field F. Let W be a subset of V then W is subspace of V over field F if…

Q: Let A = {(0, –1,6); (–1,0,2); (2,1,0)} . Then A is a basis for

A: Introduction: A set of vectors in V is the basis of V if the set is linearly independent in V.

Q: ation (1+xcos 2y)dr-x'sin 2 ydy = 0. %3D

A:

Q: Find the value of the following integral bynumerical and analytical methods over the period [1,5]…

A: Given the integral ∫151xdx Here,  fx=1x n=4 a=1, b=5

Q: Let points A, B, C be located as below. Construct the harmonic conjugate of C with respect to A and…

A: Given: Points A, B, C To find: Harmonic conjugate

Q: Consider the linear transformation T : R2[x] → R2[x] given by T(a + bx + cx2 ) = (a − b − 2c) + (b +…

A:

Q: 1 - x 1 2 - y = z +1 and l2 : х — Consider the lines l1 : = y – 2 = 3 || 2.

A:

Q: The Fourier Integral Representation of f(t) is (0, t1 f(t) 1 [sin w + 1 -(cos w wt 1 [sin w + 1…

A:

Q: 4- Calculate the substitution using SSm y dxdy -if the set M is given by inequalities x² + y° < 4x,…

A: We have x2+y2≤4x⇒x2-4x+4-4 +y2≤0⇒(x-2)2+y2 ≤4⇒(x-2)2+y2 ≤22    ( represent the region inside the…

Q: Example: A. Find the polar and exponential form of the following: 2. z = -1/2– V3/2i 3. z = -i

A:

Q: tind the rematning f the spherical trianglet a = 116*23'08" B = 127° 30'52", =900

A: The important thing to be noted about spherical triangles is that the sides of a spherical triangle,…

Q: sinca)-dx

A: Numerical Analysis Question.

Q: 7 Celia is planning to invest $20000 in the United States. The inflation rate is projected to be…

A:

Q: Consider the following optimisation problem max f(r, y) = t/r y, subject to tx? + y 0, y > 0. a)…

A: Given: max fx,y=txysubject to x2+ty≤5x≥0,y≥0 To find: a) t=1 b) Envelope theorem c) Marginal effect…

Q: Let V be a vector space of dimension 4, and let W be a vector space of dimension 2. Let L:VW be a…

A:

Q: Miss Gray is handling a group of 10 children in a school for special children. In how many different…

A:

Q: Let u = (0, –2, 2), v = (1, 3, –1) and w = (2, 2, 2). If x = (0, –2, 2), then a = au + Bv + yw. O A.…

A: Given x=0, -2, 2, u=0, -2, 2, v=1, 3, -1, w=2, 2, 2 x=αu+βv+γw We will find the value of γ

Q: 1. Evaluate the following integrals. b. I – 2.x² +1 dx

A: Properties of integral  ∫xndx=xn+1n+1+C∫[af(t)+bg(t)]dt=a∫f(t)dt+b∫g(t)dt∫f(g(x))g'(x)dx=∫f(t)dt

Q: Which of the following is not a vector space?    A. The set of all 2x2 with integer entries and…

A:

Q: 8. Use finite differences method to classify the following relations as linear, quadratic or…

A: In this question, the concept of the finite differences method is applied. Finite Difference Method…

Q: Let P be an m × m matrix with entries in the polynomial algebra F [x]. L:1.1.

A:

Q: Let M = {a E R: a <-1}. Then M is a vector space under standard addition and scalar multiplication…

A:

Q: Suppose that for a company manufacturing bluetooth and wireless headsets, the cost and revenue…

A:

Q: Evaluate the integral using Simpson's 1/3 and Simpson's 3/8 with n%3D11. Express the answer in four…

A: Simpson's 13 rule: We need to evaluate ∫14x-1 dx with n=11 Now, h=b-an We have a=1, b=4, n=11 So,…

Q: 1. In the right triangle ABC, AB = 2, BC = 4 and ED is a line parallel to AB. Find the angle a =…

A:

Q: Let A be an mxn matrix. Consider the following statements: 1. The set of solutions of the system of…

A:

Q: VA – 3 4 2x + 1 X

A: To find the value of the given integral by substitution method. Here we change the dx to dz and then…

Q: (x-3)(x+3) Graph the rational function f(x) = Find all horizontal and vertical asymptotes and…

A: Given function is fx =x-3x+32x+1x-2x-5

Q: Which of the following is true? 1 1 O A. is a basis for M22. 0 0 1 1 OB{(; ")·(: :)·(; :)·(: )} 0 1…

A:

Q: Find the Inverse Laplace Transform 38-16 82 -24s+69

A:

Q: B. Solve. Two hikers start at the visitor center. The first hikes 4 miles due west, then turns 40°…

A:

Q: b What is the general solution of the differential equation? Reason out why it is the general…

A:

Q: The determinant of P is a non – zero scalar polynomial.

A:

Q: (b) Express the integrands as a sum of partial fractions and evaluate the integral de -x*-6x (a)…

A:

Q: are fields of subsets of 2, then F1N F2 is 3.15 Prove that if F1 and F2 also a field.

A:

Q: Solve the nonhomogeneous y'+ 2y equation

A:

Q: (a) For each c, find a basis for the columns space of A. (b) For each c, find a basis for the null…

A: This is a problem of linear transformation.

Q: 9. Find the radius of convergence, R, of the series. Find the interval of convergence of the series.…

A:

Q: e Petermind is Hhis seriese Geometnic not emd Amd asumof it - 27-9 +371,..

A:

Q: A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A. 3…

A:

Q: Which of the following ordered pair is a solution to the given inequality? -4 -3 -2 -1 12 -1 2x - 5y…

A:

Q: Find the Taylor series generated by f at x = a. 1 f(x) = -, a =5 X (- 1)"(x- 5)" O A. E 5h + 1 n = 0…

A:

Q: (a) Divide r – xª + 3x3 + 2x2 and remainder r(x). Verify that the quotient times x – x? + 1 plus the…

A: Introduction: A polynomial is a very important real-valued function. The degree of a polynomial is…

Q: +y = e* + cosh 2x+x +y%3D

A: Solution:-As per guidelines I submit first question only

Q: 1. Solve for x:

A: When a secant through an external point M meets a circle at two points, then the product of the…

Q: Consider the series E 1+* (a) Find the series' radius and interval of convergence. (b) For what…

A: We have given a series ,  ∑n=1∞ 1 + 1n6n x9n Here , an = 1 + 1n6n x9n (a) We need to find interval…

Q: Let f(x) = 2" + x. Find (f-1)'(1).

A:

Q: = { (; ):a,b eR }with the standard operations in M22. Let W Which of the following statements is…

A: Lets solve the question