Find the extremum of f(x,y) = 5x²y² +5y² + 6x?. Answer:

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

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Q: On what interval is the curve t2 X. dt y% = Jo t2 + t +2 concave downward?

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Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle ² +y² = 13.

A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

Q: The cubic y = ax3 + bx? + cx + d tangent to the line y = 12x + 13 at (-1, 1) and have a horizontal…

A: Solution...

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approxim

A: Given,         f(x, y)=11-2x-y

Q: Find the greatest and smallest values that the function f(x, y) = 4x+5y takes on the circle x2 + y?…

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Q: Find the points on the surfaces z = V² + y? and z = 2 – x/2 having the shortest distance to the…

A: We know that the two given surfaces will intersect at some curve whose equation can be obtained by…

Q: At what interval is y=x^3-3/2x^2 concave upward?

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Q: Find the point in the plane x – 2y + z = 4 that is closest to the origin.

A: Solution)                   Given                           plane  x-2y+z =4

Q: Q.2/ Test the following surfaces for maxima, minima Z(x,y) = xy + 7x² – 12y°x² – 6x + 5

A: Given           Z(x,y) = xy+7x2-12y2x2 -6x+5   ...   (1)

Q: i) Pre that at the Point x- of the Crerve Y: 4m-S, the radices of cervatune f' 5is

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Q: IND THE ORTHOGONAL TRAJECTORIES OF THECURVES Y =Cx²,WHERE CIS AN ARBITRARY CONSTANT.

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Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

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Q: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a>0.

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Q: c) x+2y) dA, where D is bounded by the parabolas y=2x2 and y =1+x?.

A: C) The area D bounded by the parabolas y=2x2 & y=1+x2 is as shown below. The red graph is of…

Q: 3. Describe the level surfaces of the function. f(x, y, 2) = x² + 4y? + 42?

A: We Know that,  A level surface of a function w = f(x, y, z) with three variables is a surface f(x,…

Q: Find the extremum of f(x,y) = 9x2y² +4y² + 4x². %3D Answer:

A: Topic= Derivative the extremum is 0.

Q: Find the absolute maxlimum of frr.y)=xy subject to the Coustraint glxy)= x²ty²=/

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Q: Find the set on which the curve 7 dt t2 + 6t + 15 y = is concave downward. Answer (in interval…

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Q: Find the absolute maximum and minimum of f(x, y) = 4x2 + 2xy 3y2 on the unit square 0 sx s1, 0 sy…

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Q: Q2: A-The Trapezoidal rule for roodx 5 and Midpoint rule /)dx=4 What value does . Simpsons rule give…

A: 1st we will find relation between trapizoidal , mid point and simpson rule . Then will use this…

Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(x+y) * (xy-1).

A:

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + B.

A:

Q: express in the form y = f (x) by eliminating the parameter x = t + 3, y = 4t

A: The given parameters are x=t+3, y=4t. The objective is to express in the form y=fx by eliminating…

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

A:

Q: at what interval is  y=3x^5-5x^3 concave upward?

A: Given y=3x5-5x3

Q: Find the best quadratic approximation, Q(x, y) of V9 – 6x – 4y for (r, y) near (0,0).

A: We have to find the best quadratic approximation Q(x,y) for (x,y) near (0,0).

Q: 1. Find the absolute minimum value of 0 < x < 4 f (x, y) = 4x² + 2xy – 2y? – 18x on the rectangular…

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Q: Find the area of the segment cut off from the parabola x2 = 8y by the line x- 2y + 8 = U. %3D

A: Introduction ::

Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

A:

Q: Find the Felative Maximum vasve of Fx,x) = x*- y, Subuicct to the Construint X-Y=24.

A: The given function is as follows. fx,y=x2-7y2 the given constraint is as follows. x-y=24y=x-24 The…

Q: Find the Maximum value of the function f(x, y) = x² – y² – 2y on the curve x? + y? = 25. %3D -

A: By langrange multiplier method n

Q: The area which is enclosed by the curve x2 – 10x +4y + y² = 196 is А. 12п В. 15п C. 144 D. 225n

A:

Q: 2 5. x = 1+t2 2 y= t(1+t?)

A:

Q: Find the absolute maxima and minima of the function f (x,y)=2x²-4x+y²-4y+1 on the closed triangular…

A: Given:The given function is f(x,y)=2x2-4x+y2-4y+1 on closed triangular region bounded…

Q: Find the point on the parabola x = t, y = t²,-∞ < t < ∞o, closest to the point (2, 1/2). (Hint:…

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Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

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Q: Along the straight line x + y = 1, the function f(x,y) = xy has a local extremum at the point (0,0)…

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Q: find the points on the curve x^2+xy+y^2=16 which one nearest and farthest from the origin using…

A: Let us consider the given function f(x,y) Subjected to g(x,y)=C Solving using Lagrange's multipliers…

Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

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Q: find the dy リ=(メ+z)mx, (xを when 3In X

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Q: x² + 5x ,14.f(c) = = 14 f(x) on interval %3D %3D x - 1

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Q: Find the extremum of f(x,y) = 5x²y² +4y² + 6x². %3D Answer:

A: The given function is f(x,y)=5x2y2+4y2+6x2 .......................... (1)

Q: Find the interval on which the curve (x) = J di is concave downward. 6+ 8t

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Q: Find the isogonal trajectories to a family of straight lines y= cx that cut the lines of the given…

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Q: What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the…

A: We have to find the maximum vertical distance between the line y-x=2 and the parabola y=x2 in the…

Q: On what interval is the curve t2 dt t2 +t+2 y = concave downward?

A: The given curve is: y=∫0xt2t2+t+2dt Using fundamental theorem of Calculus says: ddx∫axf(t)dt=f(x)…

Q: Find the absolute maxima and minima of the function f(x,y)=x²+y? on the closed triangular region…

A: The given function is fx,y=x2+y2 Given lines are x=0,y=0,y+2x=2

Q: Find the largest domain (in R²) for the function 1+ Vx + Vy x² + y? f(x, y) =

A: The domain are those values of x,y; such that f(x,y) is well defined. Well defined means that the…

Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t