1. Given a two variables function z = f(x, y) = V64 – 4x2 – y2. (i) Determine the domain and range of f. (ii) Sketch the contour of f (level curves of f projected on the ry-plane) for the values of z = 0, z = V15 and z 8. (iii) Sketch the traces of f for (a) r = 0 and (b) y = 0.

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: the domain and sketch several level curves of the following functions. (x, y) = *+y x-y *+y² -1 ii)…

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Q: b) Find the slope of the function f(x) = VI+1at point (15,4).

A: The slope of  f(x) at a point (a,b) or x=a and f(a)=b is given by, df(x)dxx=a or f'(a)

Q: The level curves of the function f (x, y) = /2x² + y² – 1 are

A: Explanation of the answer is as follows

Q: Let f: R² → R be a differentiable function. (a) At the point (ro. Yo) = (1,5), it is known that the…

A: Given That : Equation of tangent plane to the surface z=fx , y is -2x+3y-z=17. To Find : a)…

Q: 1. Consider the function : = f(x, y) = V16 – r - 4y2. (i) Find the domain and range of the function.…

A: Given function is z=f(x,y)=16-x2-4y2. Solution of (i): Square-root is defined only for non-negative…

Q: Sketch the level curves of the function f(x, y) = 6-3x - 2y for c= -6, 0, 6, 1, 2

A:

Q: Sketch a contour map of the function given by f(x,y)=x2-y2 showing the level curves at the given…

A: The graph a three dimensional surface is represented by the equation: z=f(x,y). If the graph of…

Q: Consider the relation between r and y defined by the equation r4/3+y4/3 = 10. Find the r-intercept…

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Q: Sketch the level curves of the function z(x, y) = 10- 9 8 7 6 5 4 3 -10 -9 -8 -7 -6 -4-3-2 2 4 5 6 8…

A: Level curves equation   y=-6x/5Explanation:

Q: Assume that y is a function of x. Find (d2y)/(dx2) for x2y-y2-2(sqrt x)+4=0 at point (1,2) 7/6 8/6…

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Q: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: 2. Given the function, find the slope of the line tangent to the curve: f(x) = v5x + 2 at the point…

A: We have to find the slope of the line tangent to the curve: f(x)=5x+2 at the point P(1,2) for the…

Q: 1. f (x, y) = x² + y?

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

Q: Find y' if 3x2- (xy²) = 2y³ 2 3=

A: Given: 3x2-xy212=2y3   As we know that; The sum/difference rule: f±g'=f'±g' The Power law;…

Q: Given a function f(x, y) = 3 – 9 – x² –-(y+1)². Determine the three level curves for the function…

A: We can solve as follows

Q: 1. Consider the function z = f(r, y) = V16 – r² – 4y². (i) Find the domain and range of the…

A: "Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: 3. Let f(x) = 2x - x². (a) Find the secant line to the graph of f passing through the points (0,0)…

A: We can find equation of secant line and tangent line .

Q: Considering the following graph of the given function f. y The xy-coordinate plane is given. The…

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Q: . Sketch the level curves of the function f(x, y) = x² + 2x + y² – 6y corresponding to the z-values…

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Q: f(x, y) = x² + y² (a) Determine the domain of the given function. (b) What are level curves f(x, y)…

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Q: Let f(x) = 2x² 11a + 4 - The slope of the tangent line to the graph of f(x) at the point (2, 10) is…

A: This is a problem related to derivative of the function. Please follow the procedure given below.

Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

A:

Q: If (X, d_{1}) and (Y, d_{2}) are metric spaces, we define d: (X × Y ) × (X × Y ) \rightarrow R by…

A: Let X be a nonempty set with a mapping d:X×X→R is said to be a metric space if mapping d…