g(x, y) = = sin(xy) xy Prove that g is continuous on R². if (x, y) = (0,0) if x = 0 or y = 0.

Q: Q2) a) Find Maclaurin expression of f (x) = Cosh (x) b)Find the gradient of the function f(x, y, z)…

A: Part (a) General form of function fx is Maclaurin series is…

Q: given f(z)=u(x,y)+iv(x,y) is an analytic function where u(x,y)=x^3-3xy^2. find f(z)

A: We have to find .

Q: what is f'of x

A: Find f’(x).

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: Following function f(x ,y) = x3 - 3x2y + 2y2 - 12 Verify that 2* d2f / dx2 + 2*d2f / dydx +…

A: f(x,y)=x3-3x2y+2y2-12formula used is(i)  ∂ ∂x(xn)=nxn-1 (ii)  ∂ ∂x(constnat)=0

Q: If f(r, v) = ry – ry", find 7 + ±),-.y-a

A: The power rule of differentiation states that d dxxp=pxp-1, where p is any real number. Use the…

Q: f(X1,X2)= f(X,).f (X2) If X,~N(H1,0) X2~N (H2,0) are not independent then ylgn ihi

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: f(r,t) = cos(3r) exp(4t) %3D fi(x,t)+ frz(x,t) = f(r,t) %3D

A:

Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: Suppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and…

A: Solution

Q: Prove that the function ((z*)2 Iz| > 0 f (z) = z 0, z = 0 is not analytic at z = 0 by calculating…

A: Given function is f(z)=z*2z, z>00,        z=0 we have to prove, the above function is not…

Q: Let sin(4x + 7y°) x3 + y5 if (x, y) # (0,0) f(x, y) = 0. if (x, y) = (0,0) %3D Which of the…

A:

Q: If F(x,y,z)=sin(x³y²)+cos (Vxy2)+x®y²z, then fyz(1,-2,1)=

A:

Q: Let f(x, y) = x/y. Then the directional derivative of f in the direction of √2 point (1, 1) is ○ (1,…

A:

Q: Prove that the function (z*)2 1리 > 0 0, z = 0 f (z) = is not analytic at z = 0 by calculating all…

A: Calculate the derivative of fz at z=0.  f'0=limZ→0fz-f0z-0       =limZ→0z*2/z-0z-0       =limZ→0z*z2

Q: 6. Show that f(x) = sin x is uniformly continous on R.

A:

Q: Assume that R (t) + 0. Show that T'(1) = R' (t) – (De||R (t)|)Ť(t) T'(t : ||T (t)||

A: As per the question (and the general conventions in vector calculus) we have a vector valued curve…

Q: Determine if f(x, y) = xe*-y + 100y is increasing or decreasing at (-2,1) if a) we allow x to vary…

A:

Q: af If f(x,y) = sin-(4x³y?) then dx 12x?y? 1-(4x³y²)² O a. b. 1 4x³y²/(4x³y?)² – 1 c. 12x²y² 4x³y?…

A:

Q: 2. At what points of R² is the function continuous? (sin(x² + y²) x² + y² f(x, y) = 0, -, if (x, y)…

A:

Q: f[x'+zy2,y²2x2], then prove that [y?-zx] (a?-yz] dy [z-xy] du -o. If

A:

Q: Show that the function g(x, y) = is not continuous at (0,0). xy 2x² + y²¹ 0, (x, y) = (0,0) (x, y) =…

A: g(x,y)=(xy/(2x2+y2), (x, y) not equal to (0,0)               0                 ,(x, y) = (0,0)

Q: Let f(1,y) = (r+ay°,r²y°,2r + by), g(u, v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: Let f(x, y)=x3+ay2, x2y3, 2x+by,  gu, v, w=3u2+bv2+w3, uvw. We need to find the derivative of fgu,…

Q: (x³ + bx + a, xs-1 lbx? - Let f(x) = .Then the values of a and b so that the %3D -a, x >-1…

A: The function is: f(x)=x3+bx+a, x≤-1bx2-a,      x>-1 So, the function is continuous at x=-1 if…

Q: I. Determine whether or not the function x2 + 2y if (x, y) # (0,0) f(x, y) 1 er-y if (x, y) = (0,0)…

A:

Q: The maximum directional derivative of f (x, y, z) = x² sin(zy) – yx + 10 | at (-1, 2, 0) is

A:

Q: Determine if f(x, y) is continuous at (1, 0) where (x - 1)²y² (x − 1)² + y² - 0 f(x, y) = = if (x,…

A:

Q: 2x'y+x?y? + 3xy³ 16x4 – y4 if (x, y) # (0,0) Let f(x, y) = if (x, y) = (0,0) Determine the set of…

A:

Q: I+2y 2. r2 = %3D I-2y

A: We have to find the differentiation y'.     According to our guidelines we can solve only one…