x Sketch the level curves of the function f(x, y) = 4 y for c = 9 -9, –4, – 1,0. -

Q: Find an equation for the level surface of the function f(x,y,z) = In ху that passes through the…

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Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: Given: x=et……1y=te-t……2 where t≥0   To find: Slope of line tangent at x=3

Q: find the directions in which the functions increase and decrease most rapidly at P0 . Then find the…

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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: Consider the function 8 · + 9. xy f(x, y) In which direction does the function f(x, y) increase most…

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Q: Q.1. Justify why the level curves very close to the origin (0, 0) for the function f(r, y) =…

A: To find the level curves, equate the function fx,y with a constant C.

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: Find the maximum rate of change of the following function at the given point. f(x, y, z) = x² + 5xz…

A: To Determine: find the maximum rate of change of the following function at the given point . Given:…

Q: (c) The tangent plane to the graph of z. = f(x, y) at the point (1, 0, 1) can be described by the…

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Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If doesn't exist…

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Q: Find y as a function of t if y" + y' – 2y = 0, y(0) = 8, y(1) = 8. y(t) = Remark: The initial…

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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: 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: Find a function f(x,y,z) whose level surface f=8 is the graph of the function g(x,y)=6x+7y f(x,y,z)…

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Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: define y as a differentiable function of x,  find the value of dy/dx at the given point. 25. (x3 -…

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Q: (b) The tangent plane to the graph of z = f (x, y) at the point (1, 0, 1) can be described the…

A: We need to find the tangent plane to the graph of f(x,y)=e3yx4 at the point (1,0,1)

Q: Let f'(z) = tangent line to the graph of the function h(z) = g(13x+3) at e and g(x) = f(/#). Let L…

A: Given, f'x = ex2  gx = fx L is the slope of the tangent line to the graph of function hx = g13x+3 at…

Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x+4) in the interval…

A: Given: y=2x-123x+4

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: We will use chain rule of partial derivative  If F is a function of  two independent variables x and…

Q: Find the linear approximation to the equation f(x, y) = 4 ln(x¹ −y) at the point (3,80,0), and use…

A: Linear approximation

Q: .Find extrema for a function y=f(x)%3D2X² - 8x on an interval [0, 6].

A: An extremum (or extreme value) of a function is a point at which a maximum or minimum value of the…

Q: Find the vertical trace of the function at x = 1: g(x, y) = cos√x² + y²

A: Definition : Consider a function z=f(x,y) with domain D⊆R2. A vertical trace of the function can be…

Q: xy The level curves of the function f (x, y) x2 +1 O optio O option

A: A level curve of a function is curve of points where function have constant values. Z=f(x,y)  then…

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

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Q: Find the absolute maximum and minimum values of the following functions on the given curves.…

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Q: Find the maximum slope on the graph of f(x, y) = 4 sin(xy) at the point P(5, 0). 1. max slope 20T 2.…

A: Given:- f(x, y) = 4 sin(xy) To find:- Find the maximum slope on the graph of f(x, y) = 4 sin(xy) at…

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

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Q: 1. Given z = f(x, y) = √x² + y² + 4y. (a) Find its domain and range. (b) Sketch the level curves for…

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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: Sketch the level curve of g(x,y) = y / 4 ln x corresponding to g(x,y) = -1/2

A: g(x,y)=y4ln x=-12⇒2y=-4ln x⇒y=-2ln x

Q: Find the absolute maximum and absolute minimum values of f on the given interval. fix) =Dx + 는,…

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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: Sketch the graph of function f(x, v)- J4-x - and draw the level curves at k- 0, 1,4

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

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Q: The function 5· x. y g(x, y) -20 · y + 2· x + 6 is continuous everywhere on R? except on a line I in…

A: The given function is: g(x,y)=5xy-20y+2x+6...(1)

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

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Q: In r d) y = (V)" at (1, 1)

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

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Q: Find the absolute extrema of the function y tan( on the closed interval [0, 2]. %3D 8.

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

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Q: 3. The temperature on a portion of the surface of a metal plate is given by T(x, y) = 4 x² + 2y3 +…

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Q: Find the orthogonal trajectories of the given family of curves. 1. y = c (sec x + tan x )

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Q: 3. Find the value of c such that the line y = x + 3 is tangent to the curve y = cvx. C =

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Q: 7 Find the value of c such that the line y =-x + 7 is tangent to the curve y = cyx. 4 с 3

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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: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

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Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x + 4) in the interval…

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