(b) Evaluate (3, 10) J(0, 1) Cto (3x + y) dx +(2y - x) dy along- @ curve y= x? +1; (ü) the line joining (0, 1) and (3, 10

Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

Q: If f(x, y, z) = 16xy – 4yz – 4zx + 3, then the first order partial derivative fz = - - (4y + 4x) - –…

A: When a function is differentiated concerning a particular variable and the rest all the variables…

Q: 2. Find the directional derivative of o = yx2 +x²z + 3xyz in the direction of vector n = î + 2 ŷ -2·

A:

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: 2. Compute F-dr where E= (x+ y,x-2z,z- y) and curve C is the line segment from (-3,5,1) C to…

A: Using line segment as the base of a rectangle, we choose the height to be the height of the surface…

Q: 5. Deduce the standard linear approximation of 1 x2+y2+z2 at Po(1,2,3).

A: The general formula of the standard linear approximation for f(x,y,z) is generally given by,…

Q: Find the orthogonal trajectories of the famil y of curves x'yxy=c where cis constant

A: Given:    x3y-xy3=c      Differentiating by using power rule we get…

Q: (x,y) 3Dxe+3y: y(1,0)

A:

Q: (6) Find the orthogonal trajectories of the family of curves r 4C cos 0, where C being %3D…

A: We have to solve given problem:

Q: (6) Find the orthogonal trajectories of the 3C cos 0, where C family of curves r being parameter.

A: Answer

Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: 2. Find a function f(x, y) which is NOT linear in either a or y and for which the tangent plane at…

A:

Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy² = 2 (C- cos x) O…

A:

Q: (6) Find the orthogonal trajectories of the family of curves r= 2C cos 0, where C being parameter.

A: Consider the given curve. r=2Ccosθ          (1) Find the derivative of the given equation.…

Q: Could I get help finding all the second order derivatives please?

A: Given

Q: Find the given partial derivative. f(x, y) = 2 sin(6x² – y). fy(0, ) =?

A: First we find the partial derivative with respect to y

Q: Find the gradient of the function w = xy2z2,  and the maximum value of the directional derivative at…

A: Given function:    w=xy2z2

Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

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

A:

Q: Find the orthogonal trajectories of the one parameter family of curves ex+e-y=c

A:

Q: Compute the partial derivative: f(x, y) = sin(x" –- 3y) fy(0, ) =

A:

Q: 8. Find the directional derivative of f (x, y, z) = xyz3 at P(2, 1, 1) in the direction of Q(0,…

A: Ans=1 I have considered image question bcz I think you have done mistake while typing... Now go…

Q: A heart-shaped graph in a 2D plane is defined by the equation (x² + y² - 1)³= 4x²y³ Determine dy/dx…

A:

Q: Find the gradient of cos(xy) – 3y4 + 3 at the point (1,4) -

A:

Q: Find the value of at the point (1, 1, 1) if the equation xy+ z°x – 2yz = 0 defines z as a function…

A: Given equation, xy+z3x-2yz=0

Q: The

A: Below is sketch of  the given function.    Rotation about x axis will give a volume in 3D plane.

Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy²= 2 (C- cos x) O y…

A: This question is related to differential equations, we will solve it using given information.

Q: (4) Find the orthogonal trajectories of the family of curves z +y 2C?, where C being %3D a…

A: Note:-    as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Q1: Find the derivative of f(x,y,z)=x^3-xy^2-2z at point P_o (1,1,0) in the direction of vector…

A: Solution:-

Q: Q1: Find the derivative of f(x,y,z)=x^2+yx^2-3z at point P_o (1,1,0) in the direction of vector V…

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

Q: A heat-seeking particle is located at the point (2, −2) on a metal plate whose temperature at (x,y)…

A:

Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 3z) at the point (– 2, – 3, – 6). - -

A:

Q: 3. Evaluate the gradient of S(1, y, 2) = In(cosh z+ y) - arctan| at (1,y) = (7/2, 1).

A: Given that fx,y,z=lncosh x+y-z2 arctanx2y2+z2 To find the gradient of f(x,y,z) :…

Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

A:

Q: Tangent to the curve z2 2xy + x² , z = 3 , at the point ( 1, 4 , 3 )

A: Consider the curve, z2=2xy+x2 ⇒x2+2xy-z2=0

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: Find the maximum rate of change of f(x, y, z) = tan(2x + 2y + 3z) at the point (−9, 6, 2) and the…

A:

Q: Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0,–3,5)

A: Solution: The objective is to find the directional derivative of the given function

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

A:

Q: 5. Find all the second partial derivatives f(x, y) = 2x + 3y

A: To find all the second partial derivatives of: f(x,y)=y2x+3y For that, find the first partial…

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 all the second partial derivatives (including fxy etc.) a) v = sin(2s^2 − t^3)

A: Please see the explanation below

Q: (6) Find the orthogonal trajectories of the family of curves r= 5C cos 8, where C being parameter.

A: we have to find the orthogonal trajectory for the given function

Q: Find both first partial derivatives. z = 10y² Vx Oz dz %3D %3D

A:

Q: Tangent to the curve z2 = 2xy + x² , z = 3 , at the point ( 1, 4 , 3

A:

Q: Find the direotional derivative of the scalar function f-x'+ y' +2z', at the given point (1,1,2), in…

A: Explanation of the answer is as follows

Q: Find the gradient for the curve defined by y + xy = 3 at the point (1,2)

A: Gradient to given curve

Q: (b) Show that the function defined by xy √√√²+y² f(x, y) 0 if (x, y) = (0,0) is not differentiable…

A: We have to show that the function defined by…

Q: (6) Find the orthogonal trajectories of the family of curves r= 2C sin 0, where C being parameter.

A: See the detailed solution below.

Q: Find the indicated partial derivatives. f(x, y, z) = cos(5x + 7y + 3z); fxyzı fyzz 50 sin (5x + 7y +…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.