32. Match the function with its graph (labeled I–VI). Give reasons for your choices. 1 1 (a) f(x, y) (b) f(x, y) : || 1 + x? + y? 1 + x²y² (c) f(x, y) = In(x² + y³) (d) f(x, y) = cos Vr? + y?

Q: Find all values of x such that dy/ldx = 0 where y is the function stated below. x2 y = -3x + 4)

A:

Q: A particle is moving along a line, whose directed distance from its origin is given by the function…

A: f(t) is a distance function.

Q: 3. Find , 9 for the functions: ax' ây sin(x³ + y* ) x* +y , (x,y) = (0,0) f (x.y) = .(x.y) = (0,0)

A: f(x,y)=sinx3+y3x2+y2, x,y≠(0,0)0, (x,y)=(0,0)

Q: 2. Show that the function u = p(xy) + Vry (y/x) provides the equation y². 0. dy?

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: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

A:

Q: The critical point of the function* f(x, y) = x² + 5y² + 2 cos x

A:

Q: 9. Find the constants a, b and c of cubic function f (x) = ax³ + bx + c such that : • The slope of…

A: Given that, f(x) = ax3 + bx  + c Slop of tangent line at x = 3 is 0. f'(1) = 24 f(x) croses the x…

Q: – x®y³, 6. Given f(x, y) = e®° - show that fxy = fyx.

A:

Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: 4. Find f'(x), if f(x) = (2x – 8x²)-²(3x + 1). 5. If y is a twice differentiable function and x cos…

A: Differential equation. Solving only first ques as per bartleby guidelines.

Q: 4. Find if y is a function of r defined implicitly by da 2*y + sin a = xe" + In

A:

Q: 3 36 Consider a fumetion f whose first and second derivatives are f'(x) and f"(r) = 5/2 (1r² + 1)"/2…

A:

Q: find the absolute extrema of thefunction on the closed interval y=x \ln (x+3),[0,3]

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: is concave up on interval The graph of f(x)= x2 – 1 OA(-1,1) OB (0,1) oC(-1.0) U (1, 00) OP (-x,-1)U…

A: F is concave up if f’’(x) > 0.

Q: 11. Find the linear approximation to given function at indicated point (Баллов: 2) x2 z = 3 + +, Po…

A: Topic:- linear approximation

Q: dy 2- Find for the following function: dx А- у%3Dх*. сosx B- y= 2(secx)²

A: Given : A) y = x3·cosxB) y = 2secx2

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A:

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: 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: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

A:

Q: -2? + 15z - 27 f(z) = 3z2 + 7z + 6 C, I= 3 What value of C would make f(x) continuous at z = 3?

A:

Q: 2. Show that the function u p(xy) + Vry (y/x) provides the equation = 0.

A:

Q: 2. Show that the function u = (xy) + JTY v(y/x) provides the equation y² : 0. dy?

A:

Q: ,is concave up on interval x2-1 The graph of f(x)D OA (-1,1) OB. (0,1) В. Oc. (-1,0) U (1, 0) OD.…

A:

Q: 2. Find the equation of the line tangent to the curve at the point indicated. Express your answer in…

A: As we know that; The slope of the tangent line to the curve at a given point Px0,y0 is equal to the…

Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

A:

Q: Find a point zo where the function f (z) = (z – 8 – 10i) (z – 8 – 10i) is differentiable. What is…

A:

Q: Assuming that the following equations define z an implicit function of x, y and, z = f(x, y), for æ°…

A:

Q: Find the -of the following function : ду w = cos (x2 + 2 y) – e4x- z*y + y3 .A a w = 2 sin ( x2 + 2…

A:

Q: Show  that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation  =0

A:

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

A:

Q: -Determine the analytical function f(2)=u+iv if = y'. Is u(x, y) harmonic?

A: Let fz=u+iv Here, ∂v∂y=y2 We have to check whether ux,y is hormonic or not. Since, ux,y=u and vx,y=v…

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: I grad(f)•dr where C is graph of y = x² + 3x from (0,0) to (2, 14) and f (x,y) = ev/lx*•1}

A: The function is fx, y=eyx+1. Find: ∫Cgradf·dr…

Q: -2 In(x) Consider the function f(x, y) 3y

A:

Q: 1) Find the Linearization x of the function -V1+2x when x is near 0 Find the equation of the tangent…

A: As per Bartleby guideline if more than one question is asked only first question to be answered…

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: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show…

A: Given, w=f(x,y) x=rcosθ and y=rsinθ

Q: find the length of the function over the given interval x=2y, y=-1, to y=1

A:

Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

A:

Q: The tangent line to the curve y=vx-5 * for x=16 is a. y=1/8 (x+16). O b. y-4=1/6 (x-16). O c.…

A:

Q: 3 Q1// :- find fy,fy at point (4,1) for f(x,y) = Xe

A:

Q: 4. Suppose that y = y(x) is a differentiable function which is defined near x = 2, satisfies y(2) =…

A: Given x2+3xy2+y3=9y2=-1

Q: 3. If f(x) = (1–- t²)e*dt, on what interval is the curve y =f(x) upward? concave

A:

Q: xyz f(x.y.z) = et ot function is given P(2,,4) in point fux + fyy + fzz colculate.

A:

Q: 1. Consider the function f(x, y) = {√x² + y² if x # (0,0) 0 if x = (0,0) Evaluate f(x, y) over the…

A: Thank you for the question. According to our guidelines we can answer only  first question and…

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Equation of tangent line through A(x1 , y1) is given by :- y – y1 = slope x (x – x1)

Q: 9. If f(x,y) = -cos x+e*y, find Vf(x, y).

A: For the solution follow the next step.