1. Find the domain and two level curves of f(x,y) = /25 – x² – y2

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: 3. Determine the coefficients a, b, c, d that will make the curve y = ax³ + bx? + cx +d have…

A: We will find the value of a, b, c, and d as following .

Q: 4. Determine the constants a, b, and c so that the curve defined by f (x) = ax³ + bx² + c will have…

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Q: 4. Determine the maximum point of the the graph of y = 12 sin(π – 2x), for x = [-T, T).

A: Given:         y=1-2sinπ-2x     To get the maximum value of the function the derivative is equal…

Q: 4) The position function of a particle is given by F(t) = (t², 5t, tť² – 2t). When is the speed a…

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Q: Find the points at which y=f(x)=x9−17xy=f(x)=x9−17x has a global maximum and minimum on the interval…

A: We find the critical points using f'(x)=0 -1.0827 is not in the interval [0,4]

Q: FInd a so that the curve y = x3+ ax2+ 44 will have a relative extrema at (2,5). Find other extrema…

A: The given curve is y=x3+ax2+44. Since the curve has a relative extrema at (2,5), x=2 is a critical…

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: Find all points (x, y) on the graph of g(x) = 1/3 x3 - 3/2 x2 + 1 withtangent lines parallel to the…

A: Given: The function gx=x33-3x22+1, To find: All the points x,y on the graph of given function at…

Q: Find a cubic function d cx bx ax x f + + + = 2 3 ) ( whose graph has a relative minimum at (0, 1)…

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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: 1 A point is moving along the graph of the functiony = dy 9x2 + 6 such that dt = 3 centimeters per…

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Q: 2. (a) Find the linear approximation L(x, y) near the point (1, 2) of the function f (X,Y)=(0=Y) +…

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Q: 16. Let h(x, y) = xy – 2x². Find the minimum and maximum values of h on the rectangle where 0 < x <…

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Q: Find the Maximum and Minimum values of f(x, y,z) x +3y subject to the constrains x'+4y +z-36.

A: According to question,Given function,fx, y, z = x2 + 3y2,           ....1subject to the…

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: What are the control points of the splines Bezier curve from the two equations given below: a(x) =…

A: Given, ax=1+5x2+2x3...1bx=1-x+x3...2 The control points are lie on both the curves. So, to get…

Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: Calculate the maximum and minimum of the function f (x,y) = xy subject to the condition x2 + y2 = 1

A: To find the optimal solution, we will use Lagrange multiplier method. The Lagrangian function is…

Q: Determine the constants c and d in the equation of the curve y = at (0, -1) and an inflection point…

A: This question can be solved using the concept of functions and derivatives.

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

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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: Determine the coefficients a, b, c, and d, so that the curve y = ax' + bx² + cx + d have critical…

A: Since you have asked multiple questions, as per our policy we will answer first question. Please…

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: 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: 2. Find the orthogonal trajectories of the family of curves x2 + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: With y=c1.x2+k curves and curves x2+2.y2-y= c2 intersect perpendicularly. Where C1 and C2 are…

A: Given two curves are y=c1x2+k   and x2+2y2-y=c2  , where c1 &amp; c2 are arbitrary constants. Let us…

Q: Find an equation for the level surface of the function f(x,y,z) = Vx+ y - Inz through the given…

A: Solve the given

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: Let f(x,y)= 3+cos(x) sin(2y) a) Show that the function has a stationary point at (0,Pi/4). b) Is (0,…

A: To analyze the critical point (0,pi/4) of the given function of two variables

Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: 18 The curve y = (x + 2)2 has a minimum point at A (0, 4). B (4, 0). (0, -2). (-2, 0).

A: for minimum point put f'(x)=0and solve the question.

Q: 3. The cost C of manufacturing transformers in a factory varies with the output N per day according…

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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: At (0, 3), the function f (x, y) = 1 – x³ + 6x2 + y2 – 6y has a O a) None of these b) saddle point…

A: The given data is: At 0,3, the function fx,y=1-x3+6x2+y2-6y.

Q: 15 The curve y=x'+ px² +qx+r passes through the point (0, 5) and has stationary points at x= 4 and…

A: The given curve is f(x) =x3 +px2 +qx + r This curve passes through (0,5) hence it will satisfy And…

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 length of the curve between the specified interval: 3/2 a. y = x7² from x = 1 to x = 4 b. y…

A: (a) Given curve: y=x32 Interval x=1 to x=4 The length of the curve is given by the formula:…

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: 15 The curve y=xr'+px² +qx+r passes through the point (0, 5) and has stationary points at x= 4 and…

A: The given curve is  f(x) = x3 + px2 +qx + r The stationary points are that points where the curve…

Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Riemann sits on the line normal to the curve y=x2 -3x+2 at x = 1

A: Given           y=x²-3x+2 and x=1  Slope of the curve is given by =dy/dx

Q: Find the orthogonal trajectories of the family of curves x3y-xy3=c where c is constant

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Q: 18. Find the absolute maximum and absolute minimum values for the function f (x, y) = e-**-y* (x² +…

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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: i. Discuss and sketch the curve x² + 6 x = -8 y – 25 ii. For the curve y = x3 – 6 x2 + 10 - (a) Find…

A: (i) Given equation of the curve is x2+6x=-8y-25 This can be rewritten as,…

Q: 14. Find the orthogonal trajectories of the family of curves 1 y =- (x + k)³ (a) y = (3x+ C)/7 (d) y…

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Q: Find the values of constants a, b, and c so that the graph of y = ax + bx + cx has a local maximum…

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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

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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