The line that passes through the points (2,0), (0,1) is x+2y = c, where c = 1. O True False

Q: Determine D„f(4, –1,6) for f(x,y,z) = ex³y + 4zx³ in the direction of (–3,2,6). %3D

A: Given that fx,y,z=ex2y+4zx3 Then  ∇f=∂∂xi+∂∂yj+∂∂zkex2y+4zx3=2xyex2y+12zx2i+x2ex2yj+4x3k

Q: Find the domain and range of:

A: (a) We know that the domain of the square root function is always greater than equal to 0. Thus,…

Q: Suppose f(x, y) = x" + y*. Find fa(1, 1), f,(1, 1), and fz (x, y)

A: Given :f(x,y)=xy+yx

Q: 2x –1 1 , show that y"+ y' + xy +1 c) If y =-

A:

Q: А Q(1, 1) в Q(2, 0) vyQ(1, y) 3xQ(x, 2)

A:

Q: Suppose that ∇fp =〈2, −4, 4〉. Is f increasing or decreasing at P in the direction v =〈2, 1, 3〉?

A: 1) v=2,1,3 v=22+12+33 = 14 u=vv=1142,1,3

Q: If y2 is positive, then y1 + y2 will lie _______ y1 by a distance equal to ____.

A: Consider a function y=sinx+1. Here y1=sinx and y2=1>0positive.

Q: If y(x) satisfies y′′(x)=y′(x)(1−y′(x)),y′(0)=1/3,y(0)=1, then y(x)=?

A:

Q: 4. Evaluate fo (3x + y)dx + (2y – x)dy along the straight line joining (0, 1) to (2, 5).

A: We need to find the line integral ∫(0,1)(2,5)3x+ydx+2y-xdy .  We first parametrize the line segment…

Q: Find the local extreme values of ƒ(x, y) = x2y on the line x + y = 3.

A:

Q: Evaluate the line integral ∫_c (2x − y) dx − (x+ 3y) dy , where C is a straight line from (1,1) to…

A:

Q: Find fx (x,y) and  fy (x,y).  Then find fx (2, -1) and fy(-4,3)

A: The given function is fx, y=ln1+5x3y2. Obtain the partial derivatives as follows. fxx, y=∂∂x…

Q: 4. If A = 3xyz²i + 2xy³j- x²yzk and p = 3x² - yz, find (a) V-A, (b) A-V4, (c) V-(Vo) at point (1,-1,…

A:

Q: nclosed by x = y, x = 2 - y and the x-axis?

A: And: 5/6

Q: Right AXYZ with mZX XY = 12V2 Given: 45° and Find: XZ and YZ

A: Given a right angle triangle ∆XYZ and m∠X=45° and the adjacent length XY=122. To find XZ and YZ.

Q: Show that Plx-1,y) = A(x, y) X+ y-1

A:

Q: If (x, y) = (-V3, 1) , then find r and 0.

A:

Q: A curve through the point Q(4,3) has the property that the sum of the distances from each point on…

A: The distance between the points and is given by the expression . If 2 lines are perpendicular,…

Q: 1. The lines 4: x=1-t, y=2+t, z=-2-t; 12:x=3+s, y=-1+s, z = 2s are skew.

A:

Q: Find fx (x,y) and  fy (x,y).  Then find fx (2, -1) and fy(-4,3)

A: Given: f(x,y)=ln|3x4+5x2y2|∂f∂x|(2,−1)=fx(2,−1)=?∂f∂y|(−4,3)=fy(−4,3)=?

Q: set of equation: +z = 1 ay + 3z = 5 3y + az = 6

A:

Q: If F(x,y,z)=x?y-y²z3 Then fz= -3y²z2

A: Given: fx, y, z=x2y3-y2z3

Q: f(x, y, z) = 3x + 2y + 4z, x2 + 2y2 + 6z2 = 21

A:

Q: Find y' for x^4y^3−3x+2y=24 at the point (−2,1).

A: We have, x4y3−3x+2y=24 Using the chain rule of differentiation,…

Q: ) s how that the line af intersection f the Planes X+2y-22%= 5 and 5x-2y-Z=0 is Paraliel to theline…

A: Solution is written in below steps.

Q: 4. Find dyax and d2 x =V4- t , go t²-2t ye t'-2 get'.

A:

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

A:

Q: Let F(x, y) = (2xy+ y2, x² – line from (0, 1) to (2, 3) followed by the straight line from (2, 3) to…

A: The given function is Fx,y=2xy+y-2,x2-2xy-3 and C is the straight line between the points 0,1 and…

Q: Find Duf at P. 1 2. f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u %3D - -

A:

Q: 1. Evaluate 4x³ds, where C ie the line segment trom -2,-1,QL,4). らt Xz xlt)= (1-t)(-2) + t(1) E) :…

A: Introduction: A line integral is an integral that determines the function to be integrated along a…

Q: If = 2 z-x'y and A = 2x'î-3 yzj +x z'k, find A.V and A xV4 at the point ( 1,-1,1).

A: given ϕ=2z-x3y and A=2xi^-3yzj^+z2 k^ find at the point 1,-1,1 1) A·∇ϕ 2) A×∇ϕ

Q: 4. If f(x, y)=: Vx² +y? 1 , find f, and f,.

A: Given data is : fx,y=1x2+y2  To find fx and fy

Q: Find the equation of a line perpendicular to 3x – 2y = 16 that passes through the point (9, 4). - Oy…

A:

Q: Given f(x, y, z) = /2x – y – 5z, find - - f-(x, Y, z) = %3D f,(x, Y, 2) = %3D f-(x, Y, z) =

A:

Q: If A = 2.x2i – 3yzj+xz²k and o = 2z – x°y, find A.Vø at the point (1, –1, 1). |

A: The gradient is calculated using the del operator and it can be represented as ∇=∂∂xi^+∂∂yj^+∂∂zk^.…

Q: If A = 2x2'i– yzj +3xz'k and ø=x³yz, find V×(ø4)at the point (1, 0, -1).

A: Given A = 2xz2i - yzj + 3xz3k and  ϕ = x2yzSo, ϕA=  x2yz(2xz2i - yzj + 3xz3k)     =  2x3yz3i…

Q: Determine D,f (4,-1,6) for f(x,y,z) = ery + 4zx in the direction of (-3,2,6).

A: Given fx,y,z=ex2y+4zx3 in the direction of -3,2,6

Q: (i) Evaluate S(z + 5i) dz where the path is the line From z = 1 to z = 2 +i

A:

Q: e-", if 0 3,

A:

Q: Find y' for x^2y^4−3x−3y=13 at the point (−1,2)

A: Given Data: Equation: x2y4-3x-3y=13 Point: x, y=-1, 2   Differentiate the above equation with…

Q: The graph of fo- is concave down on interval (-1,1) A (0,1) B (-0,0)U(2,00) .C (-x,-1)U(1,00) .D

A: The intervals where f(x) is concave down, the tangents drawn on the curve lie above the curve.

Q: Solve Utt - c²uxx = 0, –n 0, %3D и(х, 0) %3D f(x), и(-п,t) %3D0 %3D и(п,t), и,(-п,t) %3D 0 %3Du,…

A:

Q: f (x, y, 2) = x³ /+42³y² – xyz +x² – Vz5 VI+ 42°y? – ryz+ x² – Vz5 - -

A:

Q: Compute Δy/ Δx for the interval [2,4] where y = 5x−7.

A: ∆y∆x for function y=f(x) for the interval [a,b] = f(b)-f(a)b-a

Q: Find fxy(x,y) if f(x,y)= e 4xy². fxy(x,y)=

A:

Q: If u=2x+y and v=x-2y then the st ream line is y2 x2 2ху+ 2 صواب ihi

A: Thanks for the question :)And your upvote will be really appreciable ;)

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

A: My Dear student according to the rules of Bartleby we can solve only one question post others as a…

Q: 3. If V =(3r°y-z,x²+y",-2r:'). Find grad div, at the points (2,-1,0).

A:

Q: Find a parameterization for a line passing through the points (0, 0) and (2, 8) O x=t, y = 4t Ox=t,…

A:

Q: Evaluate S. (x – y)dx + xydx where C is the y = 2x2 – 1 from the point (-1,1) to the point (2,7).

A: