Find an equation for the level curve of the function f(x,y) that passes through the given point. f(x.y) = 64 – x² - y², (2/2.v2)

Q: Find the gradient of the function f(x,y) = 4y - 9x at the point (9,3). Then sketch the gradient and…

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Q: find an equation for the line in the xy-plane thatis tangent to the curve at the point corresponding…

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Q: 2. Find the derivative of the function at PO in the direction of u. f(x,y)=6x-7y, P0(-7,-2), u=4i-3j

A: We have to find derivative

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: Suppose a person wants to travel D miles at a constant speed of (30 + x) mi/hr, where x could be…

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Q: Find the maximum rate of change of the function f(x, y) : 4y4 at the point (1,3)

A: We will solve the problem

Q: 18,8grt(10)) 10 f(x) = V2x – 2 compute the instantaneous slope at: (6, v10) Start with two points A:…

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Q: 9) Where is the function h(t) = (t + 5)"3 differentiable?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: y = x – 2 + Ce* X-

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Q: Let f(x,y) be a differentiable function satisfying the equation = xy. %3D ду af and After the change…

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Q: Find the curve length of the given functions in the given interval

A: Find dx/dt and dy/dt using product rule.Then find (dx/dt)^2 and (dy/dt)^2.

Q: Use the second-derivative test to show that the function f(x, y) = x²eY – y²e* has a saddle point at…

A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

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

A: Solve

Q: Find the absolute maximum and minimum of f(x, y) = 3z +y within the domain z² +y? < 4.

A: Use lagrange multiplier.

Q: Q3. Find the coordinates of the point(s) of the function y 3x'-5x+2, where the tangent has a…

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Q: Find the interval on which the curve dt 3 +t + 212 y = is concave upward.

A: Given: y=∫1x13+t+2t2dt

Q: Find the absolute maximum and minimum of the function on the given domain. f(x,y) = 5x + 8y on the…

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Q: Q3. Find the coordinates of the point(s) of the function y=3x – 5x +2, where the tangent has a…

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Q: Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it…

A: To find the maximum rate of change of fx,y=xlnx2+y2 at 1,2 and direction in which it occurs.  First,…

Q: Find the length of the graph of ; a. f(x)=⅓x2 -⅔ between x=2 and x=3.  b. x=cost, y=sint from t=0…

A: See the detailed solution below.

Q: Find the orthogonal trajectories of the family of curves x when 'a' is the parameter. +y Da

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Q: For function f(x, y) = 5- | 2 E find the maximum value of the directional derivative at (3, 2).

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Q: Find the maximum rate of change of the the function 80 f(x, y, z) = 1+g² + 2y? + 3z² %3D at the…

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Q: Find the absolute maximum and minimum of the function on the given domain. f(x.y) = 6x + 5y on the…

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Q: The student should determine the minimum rate of change of the function g(x, y) = y²e*Y on the…

A: First I have written the rule of minimum rate of change of a function at given point and then find…

Q: Find the orthogonal trajectories of the given family of curves. y = (1+C1 x)/(1-C1 x)

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

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Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2% D c^2. *

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Q: of the curve yln x + 5x² + y' =13 at the point (1,2) dx b) Find

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Q: Find the maximum rate of change of the function f(x, y) 3y5 x at the point (3,4)

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Q: Find the derivative of the given function at the point (a, a?, a) in the direction of w = ai + 2aj +…

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Q: Examine the function f (x, y) = x3 − 6xy + y3 for relative extrema and saddle points.

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Q: Find the gradient of the curve y = a²xe-b*x at x = 1.

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Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

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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: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

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Q: The time (in hours) that a branch of Amalgamated Entities needs to spend to meet the quota set by…

A: T(x, y)=x4+16y4-32xy+43Tx =4x3+0-32y(1)+0Tx=4x3-32yTxx =12x2-0Txx =12 x2Ty…

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

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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.…

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Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: Find an equation for the tangent plane to the graph of f(x, y) V3+ r2 – 3y2 at the point P(2, 1,…

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Q: termine the equation of the tangent line to the curve y=Vx at the point (1, A) x-4y+3=0 в) х+4у-3-0…

A: we have to find equation of tangent

Q: Find the directions in which f(r, y) = (r+y-2)2+(3x- y- 6)?, increase and decrease most rapidly at…

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Q: Find the maximum rate of change of the function f(x, y) 4y5 at the point (5,4)

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Q: Find the relative maximum and minimum values. f(x,y) = x° +y° - 3xy

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

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Q: Find an equation of the line tangent to x = t^2 −1, y = t^3 +t at the point corresponding to t = 2.

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

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Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2 = c^2. *

A: Curves:  x²+y²=c²