Find an sketch the domain of f(x,y)= 16x² – x² –4y². -

Q: Differentiate fx) with respect to g(x) of yx= xsiny

A: To find the derivative

Q: Fundamental Theorem of Calculus.

A: ∫abfx dx

Q: Find the linearization at x = a. IT f(x) = sin³ (x), a = 4

A: Given,            The linearization at x=a.             fx=sin3x, a=π4We know that,             The…

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A:

Q: What is the maximum slope of f(x,y,z)=yex-x2sin(z) at the point (0,7,5)?

A:

Q: Differentiate f(x) with respect to g(x) of yx=xsiny

A:

Q: Find the domain of analyticity for g(z) = -y3 – 3x²y + 3y + i(x³ + 3xy² - 3x).

A:

Q: find the fun Ction Y= f(x) that satisfies hp Jメ 8x² + 7 , 7, F (0) = -13 コ

A:

Q: Let f(x) = x³ + 3x2 + x + 3. Determine the points f where the tangent line is horizontal on

A: to find the points where the tangent line is horizontal we have to first derivate the function and…

Q: Find and classify the stationary points of f(x) 2x} + 4x,x3 – 10x,x, + x}

A: Given,     f(x)=2x13+4x1x22-10x1x2+x22

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: Find the direction for which directional derivative of f (x,y) = 3x² – 4xy + 2y² +29 at (-2,3) is…

A: Formula: The maximum directional derivative of f(x, y) at (a, b) is given by ∇f(a, b) and direction…

Q: 2. For what value of k will x – iky F(x, y) = (x+ y)² + be analytic?

A: Given function is fx,y=x+y2+x-ikyx+iy If it is analytic then it satisfy C-R equation ux=vyuy=-vx

Q: f(x, y) = 4x² – y²

A:

Q: () Sketch : (1) y=Jx+1 (x OSISI Isxs2 (2) y=- (-x r<0 G) y= 0sxs1

A:

Q: Find a point zo where the function f (z) = (z – 8 – 6i) (z – 8 – 6i) is differentiable. What is the…

A:

Q: B1. Verify fy = fx for the function f(x,y) = ln(2x- 3y). %3D xy

A:

Q: Consider the function f(x) = 2x³ + 71° – 8z2 – 8. Enter the antiderivative of f(x) + C

A: To find the antiderivative means integration of the given function

Q: Find and sketch the domain of f(x, y) = 9-x2-y2 Vy2-1 %3D What is the range of f?

A: We have to find the points where the function is defined.

Q: 3. Evaluate f 2xdx + (y + 2)dy along the rectangle with vertices (0, 0), (0,3), (3,3) and (0, 3).

A:

Q: Calculate the largest vertical distance between f(x) = (x + 4)² and g(x) of [- 1.66, 9.66]. 2x2 over…

A: The vertical distance between the curves is given by: (x+4)2-2x2=x2+8x+16-2x2=-x2+8x+16 We have to…

Q: Find domain a 1 f(x,y)= (1/xy) 2 f(x,y)= sqrt(y-x^2)

A:

Q: The area bounded by the curves f(x) 19x + 9 and g(x) = 19x² +9 is 3.17 square units 0.95 square…

A: Known fact: The area bounded by two curves fx  and  gx from x=a  to  x=b is given by A=∫abfx-gxdx.…

Q: Show that the function defined by xy √x²+y² f(x, y) {{ = 0 if (x, y) = (0,0) is not differentiable…

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Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

A:

Q: Find the linearization of f(x, y) = −x² + 2y² at the point (3,-1). Use the linearization to estimate…

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Q: Find for the following function: 1- y = etan'x 2-x'y+ x*y 2 at x = 2

A:

Q: Coo show that the f(x,y)=X+4xy-3y gdegrad is homogenaow of

A: Concept used: The function is homogeneous of degree n if fkx,ky=knfx,y. Given: fx,y=x3+xy2-3y3…

Q: Find an analytic function whose real part is e-x (xsiny+ycosy)

A:

Q: What is the domain of the function w = ƒ(x, y, z) = 1/xyz?

A: What is the domain of the function w = ƒ(x, y, z) = 1/xyz?

Q: Find a function flx) such that f(x) -llex and %3D 3. f(0)-- 주

A:

Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

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Q: Suppose that f(x,y,z)=x^2yz−xyz^3 is a function of three variables.

A:

Q: Supposed that z is defined implicitly as a function of x and y by the equation x2 + y2 +z2 = 4. Find…

A: The given data is: x2+y2+z2=4 To find the value of dzdx

Q: Suppose that f(x, y) = sin(4x + 6y) is a function of two variables. %3D

A:

Q: Let f (z) = (7z + 9) (i – z). What is the real part of the derivative f' (1+ i)?

A:

Q: Find the domain of f(x, y) = Vy+I y(1-x²)

A: Given: f(x,y)=y+1y1−x2 The domain of functions of two variables, f(x,y) are regions from two…

Q: Find a point 2o where the function f (2) = (z – 12 – 12i) (z – 12 – 12i)differentiable. What is the…

A:

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: Given, y=x2-1 Since it has a square root, the value inside the radical must be positive.…

Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

A:

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: Find and sketch the domain of the function. f(x, y, z) = ln(64 − 4x2 − 16y2 − z2)

A: Given function is      f(x,y,z) = ln(64-4x2-16y2-z2) We have to find the domain of this function.

Q: Find the linearization of f (x) = xe¯* at a = 0. (Hint: Remember thne product rule.)

A: Given : fx = xe-x2

Q: Found the line of differentiability of f(z)=x2 - 2xy + 3y + i(2xy - y2 +x)

A: Answer

Q: Find ý of the function x2 - e2x+3y - In(xy) = 0. %3D

A: Consider x2-e2x+3y-ln(xy3)=0We differentiate it implicity, we…

Q: Consider the function f: R²R given by f(x, y) = ³ + ² + 2xy + y2-y. Find and classify all stationary…

A: Here is the solution:

Q: Find the direction at which the function f (x, у, 2) %3 хIn(е' — хг) increases fastest at (-3,0,0)

A:

Q: Describe the domain of : f (x,y) = Ln(2 + x + y)

A: in the question it is asked to write the domain of f(x, y)=ln(2+x+y).

Q: Find a function f:R² → R, its tangent plane at the point (1; 1; f(1; 1)) is given by -2x – 9y – z+8…

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.