Use the contour map to estimate 8g/8z at the point (V8,0) for the function g(z, y) = 9-2-y2.

Q: Find the point on the surface f(x,y)=x2+y2+xy-6x+8y at which the tangent plane is horizontal.

A: Given that: f(x, y)=x2+y2+xy-6x+8y

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

A:

Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: (b) Compute the slope of the line that is parallel to the xz-plane and tangent to the surface z = x…

A: Given: Let's calculate the slope of the line tangent to the surface z=x(x+y) at the point that is…

Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: Find a direction in the xy-plane in which f(x, y) = e¹-xy has zero change at the point P(1.0. e).

A: We know directional derivative formula Du→fa, b, c=∇fa, b, c.u^ Lets say u→=cosθ, sinθ be the…

Q: Use the IVT to prove that the curves y = x2 and y = cos x intersect.

A:

Q: Evaluate y+z) ds along the curve r(t) = 2ti + tj + (4 – 2t)k, 0sts1.

A:

Q: Find the point(s) on the surface at which the tangent plane is horizontal.         z = 2xy + 3x + 5y

A: Given z= 2xy+3x+5yfind partial derivatives w.r.t  'x' and 'y' and put it equal to zero⇒dzdx=…

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction PQ. f(x,…

A:

Q: Find the linear approximation at x = 0 to Write %3D 2- your answer in the form y = Ax + B. %3D

A:

Q: Use the Chain Rule to find at aw w = x² + y² + z²; x = 10tsin s, y = 10tcos s, z = 9st² əs Find the…

A:

Q: Let f: R2 R be the function with f(xy) = x3 + y3. Determine all points € R2 such that the tangent…

A: We will use standard procedure to find tangent plane to surface, And property of parallel planes to…

Q: Sketch a contour diagram for f(x, y) = x2 − 2y2 with three labeledcontours.

A: To sketch the contour diagrams for the given function of two variables

Q: Find the directional derivative of f(x, y) = x2y3 + xy2 in the direction ~v =< −3, 7 > at the…

A: f(x, y) = x2y3 + xy2 Please see the white board for the partial derivatives at the point (-1,…

Q: Find the value of c such that the line y = (1/6)x + (3/2) is tangent to the curve y = c(sqrt(x)).

A: Solution: Y1=16x+32Y2=cx

Q: Find the linear approximation of the function f (x, y,z)= x' Vy +z° at the point (2, 3, 4) and use…

A: Given:-               Find the linear approximation function f (x,y,z)= x 3y2+z2 at the point…

Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-2, 0, 0)…

A:

Q: Find the point on the surface f(x,y)=x2+y2+xy-16x-27y at which the tangent plane is horizontal.

A:

Q: Find the derivative of f at point P in the direction of u. f(x, y, z) = 6x² + 2y – 7z?, P = (8,–6,…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the center of mass of the thin plate bounded by the y-axis and the lines y =x and y = 2 - x…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Gradient of f(x,y) is calculated by partially differentiating the equation.

Q: Find the tangent/sto the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: The equation of the parabola is given as  x+2y2+2x-y-3=0. On simplifying,…

Q: Find the point on the surface f(x,y)=x²+y²+xy-17x+9y at which the tangent plane is horizontal.

A:

Q: Find the point on the surface f(x,y)=x2+y2+xy-26x+29y at which the tangent plane is horizontal.

A: For Given surface f(x,y) The slope of horizontal tangent plane is equal to zero.

Q: • Find the direction in which f(x,y) = yeY increases most rapidly at the point (0, 2). %3D

A:

Q: Use the contour map to estimate dg/8x at the point (V8,0) for the function g(z, y) = V9-7-. || g(x.…

A:

Q: Find the tangent plane to the equation z 5a2 - 4y +5y at the point (5, 5, - 200)

A: The equation of the tangent plane to a surface  is given by fx(x-a)+fy(y-b)+fz(z-c)=0where (a,b,c) =…

Q: Find the Felative Maximum vasve of Fx,x) = x*- y, Subuicct to the Construint X-Y=24.

A: The given function is as follows. fx,y=x2-7y2 the given constraint is as follows. x-y=24y=x-24 The…

Q: Find the gradient of the functions below a)f(x, y) = In Vx? + y?

A: Here we will find out the required value.

Q: Find C so that the line y = 4x + 3 is tangent to the curve y x2 + C.

A: The given equations are y=4x+3 y=x2+c.

Q: Find the directional derivative of f(x, y) = x 2 + 4y 2 at the point P = (3, 2) in the direction…

A: Given, f(x,y)=x2+4y2 at the point P=(3,2)

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A:

Q: Find the points on the graph of f(x, y) = 3x 2 - xy - y 2 at which thetangent plane is horizontal.

A: Given that, fx, y=3x2-xy-y2z=3x2-xy-y2

Q: Find the derivative of the function at Po in the direction of u. f(x, y) = In(-10x - 7y), P o(-4,…

A:

Q: Find the tangent plane of the function f(x, y) = √2x² + 2y² at (1,1). Is it parallel to 2- the plane…

A:

Q: Let f(z) = V – 2. The slope of tangent line to y = f () at z = -1is %3D Answer:

A: The given function,            fx=x3-23

Q: Find the point at which the line F (t) = +t intersects the yz plane.

A: Given: An equation of a line in the parametric form is, r→t=<2,-7,7>+t<-5,-6,6> The…

Q: Find the directional derivative of f (x, y) = e" /Ty at the point (1,16) in the direction of the…

A: From the given problem:   fx,y=exxy ; p1,16   And the direction of the negative y- axis means :…

Q: Find f(x) if y = f(x) satisfies dy 50yz da %3D and the y-intercept of the curve y = f(x) is 2.

A:

Q: Plot along with its tangent a) x = 2e' y = (2t – 1)² %3D t = 0 %3D in

A: Solution a: Given parametric equation is x=2et,            (1) y=2t-12      (2) at t=0. therefore…

Q: Find the directional derivative of f at the given point in the direction indicated by the angl f(x,…

A:

Q: Find the interval on which the curve (x) = J di is concave downward. 6+ 8t

A:

Q: s to the curve y = x* at the %3D

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A:

Q: Let z=f(x,y) = y x². Find the slope of the line tangent to this surface at the point (-2, -1) and…

A: 5.

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ g(x,…

A: Given that: g(x, y, z)=xye10z,     P(4, 12, 0), Q(0,0,0)

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Given that, the function is gx,y,z=xye8z and the points are P3,12,0 and Q0,0,0.…