01: If the function w = f(x, y) and x = 2u + 3v, y = 3u – 2v, Find Wuy ?

Q: Determine whether the function t(xry, 2)=x' +y-2 (where Y,/ and Ź are s tritly greater than 0) is…

A: Use Hessian matrix

Q: 1+х f[X_, Y_] := 2 у - 1-x (1+) (у-1)2

A: We will use basic knowledge of the functions of several variable theory to answer this question.  We…

Q: Which radical function has a domain of (xe Rx≤3) and range of (y e RIy2-4)? Oy--√x+3-4 Oy--√x+3+4…

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Q: 2 3/2 (1² + 3 + 1)*/² from y = 1 to y

A: Solution

Q: g(t) = tV13-t, t<13 %3D Find any critical numbers of the function

A: Given function, g(t)=t13-t         ...(1)

Q: The domain of the function g(t) = vt – 2 is O R-{2} O [2, 00) O R о (-о, — 2) n (? m)

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Q: Find the inflection point(s) (x,y) to the function f (x) = x²+x+1 %3D x2

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Q: 2. (a) Define what it means by for y = f(x). %3D

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Q: Q3) If f(z) is analytic function and u(x, y) = x3 – 3xy find f(z)

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Q: 3. Determine the coordinates of the hole(s) in the function below. x² + 10x + 21 f (x) = х2 — х — 12

A:

Q: of Find - for the following function. and 5xy f(x.y) = e In (3y)

A: Given: Now,        ∂ ∂ xe5xyln3yTreat y as a constant=ln3y∂ ∂ xe5xy=e5xy∂ ∂ x5xy=ln3ye5xy· 5y

Q: d f'(a) for the function f(x) = 3x-2. swer: f'(a) =

A:

Q: HW 1-Find the domain for each function : (1) f(x,y)=Vy-x-2 (2) f(x,y)= In(x²+y² -4)

A: We have to find the domain from the given functions

Q: Q1) Find the local extreme values of the function f(x, y) = 3y2 - 2y - 3 x + 6xy

A: We use second order partial derivative to find maximum, minimum and saddle points

Q: Q:A- Find for the following functions: - 1- 1+secy xy 1+x* 2- If y = and t = v2x + 1 %3D

A: Topic- Derivative

Q: -16t +30t + 4 models the height of a ball t seconds of change of the function over the interval 0,2…

A:

Q: If a F (z) = xy+ i (x² – y²), what is F(-1+ 2i)?

A: The given question  is related to complex numbers.  Given F(z)=xy=xy+i(x2-y2) We need to find…

Q: On what interval(s) is the function y = –2x² + 3x/3 both increasing and concave down?

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Q: Given the function: f(z) = { 4z +1 z<0 14z +2 z20 Calculate the following values: f(- 1) = f(0) =…

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Q: (a) If e19z f (2) = z10 + 49 at how many points the function f (z)is discontinuous ?

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Consider f(x) = 3|x|, which is in R[-2, 2]. %3D b. Use the function F(x) to find ſ², f.

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Q: Vhich of the following is NOT TRUE about the function f(x, y) = e² + e"?

A:

Q: How many saddle points does the function f(x, y) 116 – 18r 66y + 9x + 11y? have? Answer: (Input 0 if…

A: Given problem:- How many saddle points does the function f(x, y) =116 - 18x - 66y + 9x2 + 11y2 have?…

Q: Find a function y(x) such that 4yy' = x and y(4) = 6

A:

Q: Find the fx(x, y) and fy(x, y) of the following function x2 — уз – y3 f(x, y) = Inxy

A: While finding partial derivative in multivariable function, if we have to find the partial…

Q: Suppose f(x, y) = 2 sin(11xy) and g(x, y, z) = v144 – x2 - - Find the following function values. f…

A: Suppose f(x, y) =2 sin(11xy) and g(x, y, z)=√(144 - x2 - y2 - z2) To find the following function…

Q: Y (s) 1 (s+1)(s−1)²

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Evaluate the function: S 4ry(6+y/2)dy

A: topic - indefinite integral

Q: If f is a positive function and f"(x) < 0 for a < xs b, show that T, < f(x) dx < M,

A: f is a positive function and f''(x)&lt;0 for a≤x≤b This tells us that f is concave down over the…

Q: Show that the function f(1) = (e¯1 + 1)¯' satisfies y' + y² = y, y(0) = }.

A: To prove: ft=e-t+1-1 is a solution of given differential equation y'+y2=y.

Q: find all possible functions with the givenderivative. y' = x2

A: Given function  y'=x2 That is dydx=x2dy=x2dx

Q: Q1- If we have the following function: f(x, y) = 5 x8 y/3 + In x + e*y find fxx fyy f xy, and f yx…

A:

Q: 4. Find all the points at which the direction of fastest increment of the function f(x, y) = x² + y²…

A: According to question,Given Function,fx, y = x2 + y2 -2x -2y

Q: a. Find the inverse of the function ƒ(x) = mx, where m is a con-stant different from zero. b. What…

A: a. given,

Q: Consider the function f(x, y) = x²y+ y³ – 75y. f has ? v at (0, 0). f has ? at (0, –5). f has ? v at…

A: The given function is  f(x,y) = x2y+y3-75y  We have to find the value of f at  1) (0,0)  2) (0,-5)…

Q: Q1) Find fyxx of the function:

A:

Q: (b) If 38 10z f (2) = (2** + 6) e then at how many points the function f (z) is not differentiable?

A: f is every where differentiable, there are no points such that the function f(z) is not…

Q: 5 Given that y is a function of x, differentiate the expression (x + y) with respect to x. Enter D…

A: The objective of the question is determine the derivative of the given function.

Q: J 3(x)is even function

A: Bessel Function The property of Bessel function says that- (1) Jnx is an even function when n is…

Q: 14. Given the function f (x) = x² + Vx, calculate (f-1)'(18). %3|

A:

Q: B2. Write the following beam deflection for a beam of length L = 4 m as a piecewise function y = 2x…

A: The unit function Hx-a is defined as :Hx-a=0   for x&lt;a1   for x≥aHx-3=0  for x&lt;31  for x≥3

Q: For what values of m does the function y = e™* satisfying the following equation y" – 3y' – 10y = 0?

A: Given,            y=emx and the equation is y''-3y'-10y=0.To find : The value of m that satisfy the…

Q: Q3) Draw the following functions: (3-x, xS1 5, 1sxS0 2x,x >1 1)f(x) = EX 2)y = sec

A: We have piece wise defined function fx. we have to Draw the function by giving inputs x from defined…

Q: of find and of For the function f(x,y) = x+ 8y ду

A: Function given is- f(x,y)=6x+8y To find- ∂f∂x and ∂f∂y ∂f∂x=Partial derivative with respect to  x…

Q: Find all the extreme values and their types from the function f defined by f (x, y) = 2y3 + 2x3 -…

A: Given: f (x, y) = 2y3 + 2x3 - 3xy2 - 12x

Q: Q3) If f(z) is analytic function and u(x, y) = x - 3xy find f(z) |

A: We have to find analytic function using C-R equation.

Q: 19. Given the following functions: y = 8x – x2 and y = 3x %3D | Find their points of intersection.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: y2 For function f (x, y) = x2+1

A:

Q: 3. Given the function y = x/3f (x) – 1. If f(2) = and dy %3D 11 for x = 2, determine %D f'(2).

A: Differentiation at given value