3. Let f(x,y)=x²y/(x² + y²). (a) Show that f(x,y) goes to zero if (x,y) goes to (0,0) along any straight line y = mx . (b) Show that f(x,y) goes to along the parabola y = x². 11/21 (c) What conclusion do you draw? if (x,y) goes to (0,0)

Q: the line (x/a)+(y/b)=1 moves in such a way that (1/a\power{2})+(1/b\power{2})=(1/c\power{2}) ,where…

A: Variable line is                xa+yb=1                 ......(1)Any line perpendicular to (i) and…

Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: Suppose that f(æ, y) = e" = e-3z? - 4y? +y

A:

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: Consider a spacecraft orbiting a space station that is at the point (5,7). The position function of…

A: As without any outer force a spacecraft will move along tangent line to the path it follows .We need…

Q: -2+z) ds over t e point (0, 0, 0)

A:

Q: √x² + y² x-1 (a) Find and sketch the domain of f (x, y). 2. Consider the function f (x, y) = 4 (b)…

A: The given function is  f(x,y)= x2 +y2-4x-1 We know that the domain of a function is the set of…

Q: Let f(x, y) = = 160 - 2x² - 4y² For which value(s) of y is f(-3, y) = 7? y =

A: Given function

Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: Evaluate A = F. dr where F(x, y) = (6x – 2y)i+x²j for each of the following curves. a) C is the line…

A:

Q: 3. Show that f(x, y, z) fxx + fyy+fzz = 0. = 1 x² + y² + z² satisfies the equation

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Q: Graph and shade the domain of f(x, y) = vy + x² – 2.

A:

Q: 4. A) Factor f(x) into linear factors given that k is a zero of f(x). B) Find all roots of the…

A: f(x)=6x3+19x2+8x-5, k=-1To:a) Factor f(x) into linear factors b)Find all roots of the function

Q: Let f(x,y) = 8x - 2y + 5. Find the following values of f(x,y) for the given coordinates. (a) f(2,…

A: Given  f(x,y)=8x-2y+5 Find:f(2,-1) Substituting x=2 and y=-1 in the given equation, we get  f(2,…

Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

A:

Q: 20) For the the function f(x) 5x-2, find f(4a+ 1) A) a-1 C) 9a-3 B) 20a - 1 E) 20a + 3 D) 9a – 1

A: Given that  f(x)=5x-2 Find f(4a+1)

Q: Let f(x, y) = 3x² + 4y? – axy. (a) Find the values of a such that the graph of f increases when…

A:

Q: + y = 2. What is y" at the point (1, 1)? y ² Suppose that x +

A:

Q: For f(r, v) = + find f(3,4) and state the domain of S(1, y).

A: We are given the two variable function here. To find the value f(3,4) we will simply put x=3 and…

Q: f(x) = xª -4 and Perpendicular to the line x - 4y + 1= 0.

A:

Q: For two points (x1, y1) and  (x2, y2) such that xi > 0, yi > 0 for i = 1, 2, we say  (x2,…

A: There are about 4 functions provided.To show:They are Schur convex or not.Concept used:i) Any…

Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

A:

Q: 9) Find a linear function of the form f(x) = ax +b that satisfy the conditions A-4) = 8 and (3) - 9.

A: f(x) = ax+bf(-4) = 8→ -4a+b = 8.........................1f(3) = 9→3a +b =…

Q: Sketch the domain of f(x, y) = √4x² - y² x - y² on the ry-plane.

A:

Q: If B = x°ya, + (2x + y)a, – (y – 2)a, find (a) V B (b) V X B (c) V (V B) (d) V x V X B

A: Given : B=x2yax +(2x2+y)ay - (y-z)az

Q: Find the orthogonal trajectories of the family of 2 curves x² + y² = cy A B Ⓒ с D none of the…

A: Given curve x2+y2=cy

Q: If f(x, y)= xe2y +y, evaluate grad f •dr where C is the straight line joining the point (2,0) to the…

A: