gradients vector; z= ((1/2)- (x^2- y^2))-(e^(1- x^2 - y^2) - Find the gradient and explain your observations about where the gradient is pointing.

Q: the first derivative of a continuous function y=f(x) is y'=x(x-12)^2 .find y'' and then use the grap...

A:

Q: CONVERT THE GIVEN COMPLEX NUMBERS: 1. A = 6+7i POLAR FORM 2. B = 5230 → RECTANGULAR FORM 3. C = 15 –...

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three sub-...

Q: Consider the points A(3, –1,3), B(4, –3,0), C(-2, –2, 0), and D(6,3, –5). (a) Find the volume of the...

A: given points A3,-1,3 , B4,-3,0 , C-2,-2,0 and D6,3,-5 (a) find the volume of parallelopiped that has...

Q: Given a natural number c ∈ N. On natural numbers, the relation Rc is defined as follows: ∀ a, b ∈ N...

A: (a) let (a,a) be in Rc .      Then there exist integers u and v such that       au + av = c      =&g...

Q: Fill in the missing entries to complete the matrix representation of the given graph. 1 2 3 4 5 5 . ...

A:

Q: The figure below shows an arrow diagram of a partial order R. R b a e List the maximal elements in t...

A: Given:   The arrow diagram  

Q: ôu a?u Let u be the unique solution of where (x, t) e (0, 1) x (0, 0), u(x, 0) = %3D sin Tx, x e (0,...

A:

Q: A wedge is cut out of a circular cylinder of radius 14 by two planes. One plane is perpendicular to ...

A:

Q: Compute the flux of the vector field i = -2i+ j- 2 k through the rectangular region shown below, ass...

A:

Q: Suppose that over a certain region of space the electrical potential V is given by the following equ...

A:

Q: a) ] Let W = span{(1, 1,0), (1,0, 1), (2, 1, 1), (0, 1, –1)}. i. Is (9,0,9) in W? Justify your answe...

A: according to our guidelines we can answer only three subparts, or first question and rest can be rep...

Q: 1. Consi der the power series (2r+3)" Σ V2n2 n=1 1 (a) Determine the interval and radius of converge...

A:

Q: Problem 3. * latch the following guess solutions y, for the method of undetermined coefficients with...

A:

Q: Consider the region R bounded by the curve y = In(r), the r- axis and the line = 5. %3D 3. Determine...

A:

Q: CsC 630°

A:

Q: V12(–1)" 37 (2n + 1) 1. Consider the series n=1 Use any test for convergence/divergence to show that...

A: We will use alternating series test to check series is convergent or not  Suppose that we have a ser...

Q: Find the Laplace transform of sin t cos t

A: Given f(t) = sin t cos t = 2sintcost2 = sin(2t)2

Q: Find all distinct eigenvalues of A. Then find the basic eigenvectors of A corresponding to each eige...

A: Given matrix is A = 7-108-11

Q: 7.3 0.2 -3.7 1. Diagonalize A = -11.5 1.0 5.5 17.7 1.8 -9.31

A:

Q: Question 1 State the order and linearity of the following differential equations i) cos(x²y) y" + 5x...

A:

Q: A, is skew-symmetric, then prove that (B B + B, B') An = . Ajk = 0. %3D

A:

Q: The objective is to determine graphically whether the Newton's method succeeds or fails for the foll...

A: Note:- 1. Newton method will be fail if slope of tangent is zero that is,  f'x =0 2. At local maxima...

Q: 2: Change the order of integration. •ln 4 f(u, у)dydx.

A:

Q: + y = a² (Figure 1), traversed in the counterclockwise direction. YA C R Figure 1. 1 Add file Q2: * ...

A:

Q: Apply Gauss Seidal me thod to Sulve the fotlowing Lineor equations 5 X-2 Xz -2X1 + loXz-2X3=-60 =18 ...

A:

Q: Use determinants to find out if the matrix is invertible. 20 2 4 - 6 10 -9 The determinant of the ma...

A:

Q: Q2) Find all the local maxima, local minima, and saddle points of the function: f(x, y) = x2 + xy + ...

A: Let us consider the function f(x ,y), to determine the local maxima, minima and saddle point  Find ...

Q: Use substitution technique (Vp+qx + x² = z – x) to show that dx 1 Vr2 + x + 2 +x – /2 - In Vx² + x +...

A: see the attachments

Q: Construct proofs to show that the following symbolic arguments are valid. Commas mark the breaks bet...

A:

Q: What is the laplace transformation of f(t) = ta+b + acosh√ 2t +bsinh√ 2t

A:

Q: The loudness of sound (L, measured in decibels) perceived by the human ear depends upon intensity le...

A:

Q: ipounded instantaneous interest rate curve is given by 6. Assume that the ri(t) = 0.02 + 0.05 In(1 +...

A: Given :The Continuously compounded zero rate curveri (t) = 0.02 + 0.05 ln(1+0.2t)  

Q: hinormal of the curve traced by Q makes an angle tan- (cp/o V(c2 + o?)} with PQ.

A:

Q: a b c a b c If def=2, find the determinant of g hi g hi de f The determinant is

A: The solution is given as  

Q: Find the determinant by row reduction to echelon form. 1 -1 9 6 0 1 -7 3 - 1 0 - 8 4 4 -4 30 0 Use r...

A:

Q: 1. Determine for y(s) if y(0)=3, y'(0)=-2 and y"(0)=7 dy dy dy +5 + 6- =D0 dt dt3 dt2

A: We have given differential equation, d3ydt3 + 5d2ydt2 + 6dydt = 0  It's Auxiliary equation is given ...

Q: 2п 2п 3. Find the fourth roots of 16 [cos(3 Hisin(). 3

A: Solution:-

Q: ELEMENTARY APPLICATIONS OF DIFFERENTIAL EQUATION (DILLUTE AND MIXTURE) Lake Taal has a volume of 45...

A:

Q: Use trigonometric identities to find general solutions of the equation. y" +49y = sin "x The general...

A:

Q: Problem 18. Show that dz < 2ne? 1/31 +3

A:

Q: Find the derivative of the function. 2x F(x) = arctan(t) dt Vx F'(x) : %D

A: The given problem is to find the derivative of the given definite integral function. We have to use ...

Q: 8. Consider the region bounded by y =- * , y = Vx, x=1. х

A: Let us consider the curve y=f(x) and y=g(x) The area under the curve y=f(x) and y=g(x) in the interv...

Q: Use the discrete logarithm with base g = 3 to find the square roots of 5 in F19.

A: This is a problem of the discrete logarithm.

Q: Use the method of variation of parameters to find a particular solution of the following differentia...

A:

Q: Proofs must be clear, coherent, concise, and complete, and examples should be verified to satisfy re...

A:

Q: Find F'(x) if F(x) = cot-1 Your answer

A:

Q: 3m Sin

A:

Q: -31 2: -6 -2 Find the eigenvalues and eigenvectors ofA = 特後值 -2

A:

Q: #+ )= 2 c(-)-2 sin (- 2 cos (#)-2 sin() 2 cas ()+32 sin () # + )F 2 ccs (2 sin () 27 (0) 27T +j2 sin...

A:

Q: dy -1+2, dx xx (a) Solve the homogeneous differential equation (b) Determine whether the following d...

A: (a) The given differential equation is :                                dydx = 1+yx+y2x2     ..........