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: a point Q(x2, y2) is on the line segment passing through R(-2,5) and S(4,1). Find the coordinates of…

A: Given: Given that the point Qx,y is on the line segment passing through R-2,5 and S4,1 Point Q is…

Q: Find a quadratic equation whose product of roots x, and x₂ is X₂ equal to 4 and satisfying the…

A:

Q: What curve is described by the function (t) = (2t + 3) + i(t - 5), 0 ≤ t ≤ 1

A: Step:-1 Given parametric function is ft =2t +3 +i t-5,  0≤t≤1 Here,  x=2t +3  ---(1)y=t-5  ---(2)…

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A: We have to find the maximal value of the function  on the circle of equation

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: Differentiate in two ways: y = (x + ¹)(x - ² + 1)

A: We know that the product rules of the derivative d/dx(uv)=u*(dv)/(dx)+v*(du)/(dx)

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: Calculate (4x² + Se) dy, where C is the triangle of vertices (0,0), (2,0) and (2,2). [(4x²+ Note:…

A:

Q: Find: U(x1, x2) = 2X1X2 O X1X2 2x1 2 2x2

A:

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

A:

Q: Lt² V4-t² dt V(4-x)/(2\x) x(4-x)

A:

Q: Q4) Find the linearization of: f(x) = x³ + 10 when a = -3

A: l(x)=f(a)+f'(a)

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: Prove that if x+y=%30 then y=-x

A: See the attachment

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

A:

Q: Find the domain of the function f(x, y) = In(3x? – 2y + 1). The set of all ordered pairs (x. y) for…

A:

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

A:

Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

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 all zeros of f(x) = a + 4x² + x + 4. Enter the zeros separated by commas.

A: