Plot the level curves for c = -2, -1, 0, 1, 2, for the function f(x, y) = 5x + 2y2 using geogebra

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 a function f (x, y) that has the line y = 3x - 4 as a level curve.

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 21, (1, 4,…

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Q: Sketch in the two level curves of: f (x, y) = y+ x² = k _for k = 1, 2.

A: Solution is written in below steps.

Q: f(x, y, z) = x² + 3y² + 5z?

A: Let us assume f(x,y,z)=x2+3y2+5z2=k Assume that k≠0 x2+3y2+5z2=k Divide both sides by k,…

Q: Find an equation of the plane tangent to the graph of g(r, y) = 3ev²-z² at the point where (x, y) =…

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Q: Classify all level curves of f(x, y) = Vy² – x² and draw its contour map.

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Q: Calculate the are between curves defined by: x=y2+1 x=0 y=-1 y=2

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Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: Find the curve in the xy-plane that has a slope at each point given by 1 and passes through the…

A: See attached file for a step by step explanation.

Q: Let f(x, y) = 3x2 – xy+ 2y2. Then an equation for the tangent plane to the graph of f at the point…

A: Given f(x,y)=3x2-xy+2y2

Q: Let us consider the level curve f(x, y) = 2. Does the point %3D (1, 2) belong to this curve.

A: Given function is, fx,y=y2x2+1....(1) Since, the level of the curve is, fx,y=2

Q: Find the sketch of the level curve flx, v)-c form and f(x.y) 100-x2-y and c- 0.

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Q: Figure out formulas for three level curves with levels 0, , 2 respectively. y = 0, 2y² x? = 1, 2y? +…

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Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = 4t2, y = t3 - 1

A: We have given curves; y = ƒ(x) . x = 4t2, y = t3 - 1

Q: Describe the level curves of: (a) f(x, y) = e4x-y (b) f(x, y) = In(4x – y) (c) f(x, y) = 3x² – 4y2…

A: (a) To decribe the  level curvesf(x, y)=e4x-y = 1 , 2 , 3, 4, 5

Q: Find the length of the curve x = y^4/16 +1/(2y^2) between y= -3 and y= -2.

A: we have to find the length of the curve . I have explained in details please see the explanation and…

Q: An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at…

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Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: Find the exact length of the curve. y2 - 16(x + 4)3, Osxs 2, y > 0

A: The given equation of the curve is y2=16x+43, 0≤x≤2, y>0. The graph of this curve in the interval…

Q: Please draw the graph that shows the cross section of the function f(x,y)=2y^3+3y^2−2x+4 and the…

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Q: Let f(x, y, z) = xyz + 3. Find an equation of the level surface that passes through the point (a)…

A: Given: fx,y,z=xyz+3 Let fx,y,z=xyz+3 the level surface are given by, xyz+3=k        ,k∈ℝ…

Q: find an equation for the level surface of the functionthrough the given point. ƒ(x, y, z) = √(x - y)…

A: given,  ƒ(x, y, z) = √(x - y) - ln z, (3, -1, 1)

Q: Determine an equation for the tangent plane to the graph of z = 2 + 2 vy + - 7 at the point (1, 2,…

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Q: Prove that the curves x2−y2=3 and xy=2 intersect at the right angle.

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Q: Find the equation of the tangent plane to the surface z = 4 号+ゾ + y² at the point (2, -3, 10)

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Q: Let f(x, y) = x 2 − y. Sketch the level curves for f = −2, 0, 1.

A: Given fx,y=x2-y

Q: Find the maximum and minimum values of f(x, y) = x² + 2y² on the quarter circle x² + y² ≤ 4 with r,…

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Q: Describe the level surfaces of the function.  f(x,y,z) = x+4y+5z

A: Consider the function: fx,y,z=x+4y+5z

Q: Sketch the contour plot of f(x, y) = 4x² + y² using level curves of height k = 0, 1, 2, 3, 4, 5.

A: Given: f(x,y)=4x2+y2 Let 4x2+y2=k. Now graph contour plot for k=0,1,2,3,4,5.

Q: Find an equation of the tangent plane to the surface at the given point. z = 5 - 2x - y, (3,-1, 1)

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Q: Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Since we have to find value of a,b,c and d

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: Find the point of inflection of the curve y = x^3 - 6x^2 - x+ 12. O (-2-6) O (2.6) O (2. -6) O…

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Q: Determine an equation for the tangent plane to the graph of z = 2 2 +2 ay+2y2 - 4 at the point…

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Q: Let C be the curve y = x³ – 3x2 + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

A: We need to find value of integral.

Q: Draw a contour map of the function f (x,y) = (y – 2x)2 showing several level curves.

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Q: Find an equation of the tangent plane to the surface at the given point. z = x2 + y2 + 4, (1,2, 9)

A: We know that the equation of tangent plane to the curve z=f(x,y) at point (a,b,c) is

Q: find and sketch the point of shortest (or longest) distance from the origin of curve…

A: We need to find and sketch the point of the shortest (or longest) distance from the origin of curve…

Q: Let f(x, y) = /3x +2y. Find the slope of the surface z f(x,y) in thex-direction at the point (4, 2).

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Q: (a) Sketch the contour plot of f(x, y)= Y using the level curves of height k = -2, -1, 0, 1, 2. X…

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Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y2 + 5z2 = 177, P =…

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Q: Find the equation of the tangent plane to the surface 4 = 1 16 at the point 9. (1,-3,2)

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Q: Let ƒ(x, y) = 2x + 3y - 4. Find the slope of the line tangent to this surface at the point (2, -1)…

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Q: (b) Show that the points of inflexion of the curve y = (x- a) (x – b) lie on the | line 3x +a =4b.

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Q: (2) find the (x,y) coordinates of all points of intersection ot the curves.

A: b.(2) Given the polar equation of two cardioids r=1+sinθ,r=1-cosθ. To find the points of…

Q: 3. Find the equation of the plane tangent to the graph of f (x, y) = 3x + 4y – xy at the point (1,…

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Q: Let f(x, y) = x2 + 2y. Sketch the level curves for f = −2, 0, 1.

A: Level curves: A level curve is defined as the cross section of the graph of z=fx,y taken at a…

Q: find the under the curve y=7-t^2 and above the t-axis

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.