find ƒx , ƒy  . 1. ƒ(x, y) = 2x2 - 3y - 4 2. ƒ(x, y) = x2 - xy + y2 3. ƒ(x, y) = (x2 - 1)(y + 2)

Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

A:

Q: Find the partial derivatives fx (3,5) fy (3,5) for the function f(x,y)= y^2/x-y

A:

Q: The cubic function y = ax3 + bx² + cx + d pass through (0, -6), (1, -2) and tangent to the line 3x –…

A:

Q: Bounded by the curve y = (x + 3)², the x axis, and the lines x =-3 and x= 0. %3D

A:

Q: Find the linearization of the function f(x,y) = ln(x3y6) at the point (x0,y0) = (4, 3). Leave all…

A: Given fx,y=lnx3y6     at (4, 3) The linear approximation in 2 variables is given by Lx, y=fa,…

Q: find the orthogonal trajectories of the family of curves x2+y2=a2

A:

Q: i) Find the orthogonal trajectories of the family of curves: y : 1+ x?

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems

Q: The curve ax4+bx3+cx2+dx+k passes thru P1 (5, –210), has a critical point at P2 (4, –416), and an…

A: Given The curve ax4+bx3+cx2+dx+k passes through P15,-210, has a critical point at P24,-416 and an…

Q: Determine a,b,c and d so that the curve y=ax^3 + bx^2 + cx + d will have a critical point at (0,-2)…

A: we have to determine a,b,c and d so that the curve y=ax3+bx2+cx+d will have a  critical point at…

Q: The Critical Point of y = xe-*

A:

Q: Find the orthogonal trajectories for the family of curves (enter your solution as an equation)…

A: Nothing

Q: 2 (a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path…

A:

Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

A:

Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

A:

Q: Find the partial derivative of fy for the function 3 f (1, y) = (3x² +y²)* 6 (3æ² + y°)? 32 (3x² +…

A: To find: The partial derivative fy of fx,y=3x2+y23. Given: The function is fx,y=3x2+y23. Concept…

Q: Find the critical point of the function: f(x, y) = 4x2 + 2y2 − xy + x

A: we have given a function f(x, y)  We have to find the critical point

Q: Find the orthogonal trajectories of x² + y² – 2cy = 0

A:

Q: g(x, y) = 6x² – 3y², (/8, /5) Gradient is f(r, y) = tan 6y (16, 2) Gradient is

A:

Q: Solve y′′(t)+2y′(t)+2y(t)=H(t); y(0)=1 ;y′(0)=0 where H(t)=2t+3 , 0≤t<1 H(t)=3t+1, t≥1

A:

Q: Find all the second partial derivatives forf (x, y) = x³y5 + 2x*y.

A: All the solutions are given below.

Q: 5. Given that 8x2 w(x, y, 2) VIVE Use partial derivatives to find the maximum percentage error in w,…

A: Given, w(x,y,z)=8x2y3 z4Percentage error in x, y and z is 1% , 3% and 4% To find: Maximum percentage…

Q: Find the orthogonal trajectories for the family of curves. (Enter your solution in the form F(x, y)…

A:

Q: 2. y = V4-x , x=0 and y=0 about the y- axis

A: Given that y=4-x2, x=0 and y=0 about the y-axis

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: 4) Find all first-order partial derivatives w = f(x,y, z) = 2x³y³ – /xyz + 4z6x y3

A:

Q: Q2 (a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path…

A:

Q: Find the first partial derivatives 3xz %3D 6x+8y

A:

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: x² + y² = (2x² + 2y² – x)', (0,¿), (cardioid) -

A:

Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

A:

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: (3z²+5z+3)dz (z- 2)(z+3) Integrate:

A: The given integral is ∫(3x2+5x+3)(x-2)(x+3)2dx

Q: Find the orthogonal trajectories of x^2+y^2−2cy=0

A:

Q: find the first and second derivatives. 1. y = -x2 + 3                                2. y = x2 + x +…

A: 1) Given thaty = -x2 + 3On differentiating y with respect to x,

Q: y" + 3y' = 0, y(0) = -2, y'(0) = 3

A: The solution is given as

Q: 6. Determine a, b, c and d so that the curve y = ax3 + bx2 + cx + d so that the curve will have a…

A: Note: Hi and thanks for your question! Unfortunately, as per our guideline, only one question should…

Q: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¬2v.

A: Given information : Family of curves :  x2 = 2y -1 +ce-2y

Q: Find both first partial derivatives. z = 6x − x2y + 8y2

A: Find both first partial derivatives. z = 6x − x2y + 8y2

Q: Determine the linearization of y = 4 – 2x at (1, 2). Then use it to approximate the value of y when…

A: It is given that, y=4-2x2  at 1,2 we have to determine the linearization of function. Then use it to…

Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: Consider a competitive market in which price adjusts to excess demand or supply and firms enter and…

A: given that                                                 dpdt=0.5qD-qs where qD is demand…

Q: Integrate f(x,y, z) = 2x – 3y² – 2z+3 over the line segment from the origin to (1, 1, 1) and over…

A: A parametric curve is a normal curve where we choose to define the curve`s x and y values in terms…

Q: Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) x2 + 2y2…

A:

Q: 3. Find general Golution y" + y= Secx

A: Given that, find the general solution y''+y=sec3x (D2 +1)y=sec3x

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: (b) Form the partial equation by eliminating function f from z = f(x?

A:

Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2 = c^2. *

A: Curves:  x²+y²=c²

Q: Make the curve y = ax4 + bx³ + cx² + dx + e pass through the point (1, -8) be tangent to the line y=…

A: