(a) Sketch the contour plot of f(x, y)= Y using the level curves of height k = -2, -1, 0, 1, 2. X 1-x² - y* exist? (b) Does Lt (x,y)(0,0) x² + y?

Q: 6. Find the absolute maximum and minimum of the function f (x, y, 2) = x + 2y on the intersection…

A:

Q: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: How can the position and the velocity of K be described at the moment that L passes through the…

A: The position of the point on the curve can be defined by the x-axis and y-axis coordinates of the…

Q: The gradient of the tangent to the curve y=flx) at the point P(2, (2)) is given by A 12) – h f(2+k)…

A: To find the gradient of the tangent to the curve y=fx at the point P2, f2.

Q: _12. What is the maximum directional derivative Daf of the function f(x,y,z) = x – y² + z² at the…

A: Let's find.

Q: Find the value of the number such that the families of curves  y =(x+c) -1  and y = a ( x+k) 1/3 are…

A: Given,

Q: Find the critical points of the functions

A: Consider the given function: Here the objective is to find the critical points of given functions.…

Q: Find the maximum rate of change of the function f(x, y, z) = xy + yz - xz at the point P,(1, -3, 4).

A: As per our guidelines we are supposed to answer only one question.

Q: (6) Find the orthogonal trajectories of the family of curves r 4C cos 0, where C being %3D…

A: We have to solve given problem:

Q: (2) Let f(x, y) = x² – y². Find the tangent line to the level curve f(x, y) = -3 at (1,2).

A:

Q: 2. Find a function f(x, y) which is NOT linear in either a or y and for which the tangent plane at…

A:

Q: (6) Find the orthogonal trajectories of the family of curves r= 2C cos 0, where C being parameter.

A: Consider the given curve. r=2Ccosθ          (1) Find the derivative of the given equation.…

Q: In Exercises 19–24, find the directions in which the functions increase and decrease most rapidly at…

A: Given function is Firstly, we will find gradient f at point (4,1,1)

Q: 2. Let f(r,y) = n: Find the maximum rate of change of f(r, y) at the point (4, 1) and the direction…

A: Given the given function is fx,y=xx-y and the point is 4,1. Apply formula for the maximum rate of…

Q: 4. Find the absolute extrema of the function f(x, y) = ry-x-3y on the triangular region with…

A: To find the absolute extrema of the function f(x,y).

Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Given: For any function y=f(x) can be expressed as x=f(y) in standardmathematical methods for…

Q: 3. Find the parametric equation for the line tangent to the curve of intersection of the surfaces x²…

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

Q: Find the partial derivativef,for the functionf(x,y) - &x+y. 1,(x.y)- 17 1,(x.y) = Sx+y Sx ,(1.y) =…

A:

Q: 2. (a) Find the linear approximation L(x, y) near the point (1, 2) of the function f (X,Y)=(0=Y) +…

A:

Q: 12. Find the absolute maximum and absolute minimum of the function f (x,y) = x² – 2xy + 2y on the…

A: Consider the function, Draw the triangular region in the XY-plane bounded by the points,

Q: Examine the function for relative extrema. (If an answer does not exist, enter DNE.) fx, у) %3D 8х2…

A: The given function is  f(x, y)=8x2+5y2-16x-10y+16

Q: A heart-shaped graph in a 2D plane is defined by the equation (x² + y² - 1)³= 4x²y³ Determine dy/dx…

A:

Q: 1 Determine the maximum value of the function fz) = 2x -x - 4 at the interval x e [-1,1]. A -4 в о C…

A:

Q: Since y"|? v0 at x = -1/2 e we have a relative minimum at the point (c, f(c)). Substitute c = 5e¬1/2…

A: Solve it

Q: 3. Given the function f(x, y, z) = In(x² + y² – 42²), find the directional derivative f, in the…

A:

Q: Find the coordinates of the point(s) at which the curve y = x-2/3 has gradient – 1/6. %3D -

A:

Q: 1. Given the function z = f(x, y) = Vry - I. (a) Find the domain and range of f(x, y). (b) Sketch…

A:

Q: (2x-y²)² (x,y) + (0,0) Let f(x,y) = x²+y4 2, (x, y) = (0,0) Find the slope of the tangent line to…

A:

Q: 7. Given (x, y)= x' + y² a) Find the derivative at P(1,1) in the direction of " = u,i +u ;j b) In…

A:

Q: (a) y' = 1 + x2 + y2 y' = 1 + x2 + y2 >v 1 and y' → - as x + 00, The only curve satisfying these…

A:

Q: 17. Determine the equation of the family of orthogonal trajectories of the the family of curves…

A:

Q: Find an equation for the level surface of the function f(x,y,z) = Vx+ y - Inz through the given…

A: Solve the given

Q: What is the equation of the curve y = ax* + bx + cx² + dx + e tangent to y = 25x (2,14), to y = 2x +…

A: By verifying options and substitution of point (-1,11) it is verifying option C

Q: 17. Determine the equation of the family of orthogonal trajectories of the the family of curves…

A: Given; y2=2x+c Now differentiate the given function with respect to x.…

Q: 3) Find the directional derivative of f(x, y) = xex-yx² at (-2,1) in the direction v=i-j B) g(x,y) =…

A: The directional derivative of the given function at p in the direction of u→ is  Duf(P)=∇f(P)·u^ Let…

Q: Find an equation for the level surface of the function f (x, y) = ln (x² + y²+ z²) that passes…

A:

Q: 1. Find the directional derivative of g(r, y, 2) = :2 - zy + 2y? at P = (2,1, -3) in the direction…

A:

Q: Draw the level curves for the function z = f(x, y) given by z = /4 – x² – y² when z = 0, 1, 2 and…

A:

Q: 2. Find the maximum value of the directional derivative, D f, of the function _2 f(x, y, z) = x´ +…

A:

Q: 2. Use suitable linearization to find the approximate value for the function at point P. f(x,y) (x-…

A:

Q: #2. Consider the function f (x, y,z) = xy+3xz² + 5y at the point (1,0, 2) (a) Find the direction in…

A:

Q: 3) Find the directional derivative of flx, y)= XeX-yx" A) at (-2,1) n the direction U=inj 8)…

A:

Q: Riemann sits on the line normal to the curve y=x2 -3x+2 at x = 1

A: Given           y=x²-3x+2 and x=1  Slope of the curve is given by =dy/dx

Q: Examine the function for relative extrema. f(x, у) %3D 8x2 +5y? - 16х — 10y + 19 (х, у, 2) %3D ( O…

A:

Q: (a) Suppose that the changes in power a and drag y are small. Use the linear approximation of f to…

A: Given: v(P,C)=2PkC13 The corresponding fractional change in speed is given as,…

Q: f(x, y, z) = = -√ x² + y² + 1 sketch level surface off when k = 2

A:

Q: (2) Find an equation for the tangent plane to the graph of z = where z = f(x, y) is implicitly…

A: Given: The function is fx,y,z=xy+xz+yz-lnz2+1-4. Calculation: Obtain thethe value of  fxx,y, fyx,y…

Q: Find the values of constants a,b.c such that the maximum value of the directional derivative of f…

A:

Q: 14. Find the orthogonal trajectories of the family of curves 1 y =- (x + k)³ (a) y = (3x+ C)/7 (d) y…

A:

Q: Find the direction in which the function f (x, y, z) = xy - In z is increasing most rapidly at the…

A: We will use directional derivative here